If Kayla can pay off up to $175 monthly for the purchase of a new television for $487.89, the interest she will pay at 23.5% compounded monthly is D. $18.87.
How the compound interest is computed?The compound interest payable on the credit card for the purchase of a new television can be computed using an online finance calculator as follows:
N (# of periods) = 3 months
I/Y (Interest per year) = 23.5%
PV (Present Value) = $487.89
PMT (Periodic Payment) = $-175
Results:
FV = $18.23
Sum of all periodic payments = $525.00
Total Interest = $18.87
Learn more about compound interests at https://brainly.com/question/24274034.
#SPJ1
As we have seen, the P-value depends on the alternative hypothesis. In general, which alternative hypothesis will give the smallest P-value?a. μd ≠ 0b. μd < 0c. Not enough information, depends on the problem.d. μd > 0
The alternative hypothesis that will give the smallest P-value is a. μd ≠ 0.
This is because the alternative hypothesis μd ≠ 0 is a two-tailed test, meaning that it considers both the possibility of μd being less than 0 and greater than 0.
This means that there are two areas in the tail of the distribution that are considered when calculating the P-value, leading to a smaller P-value.The other two alternative hypotheses, μd < 0 and μd > 0, are one-tailed tests and only consider one area in the tail of the distribution, leading to larger P-values.
Therefore, the alternative hypothesis μd ≠ 0 will give the smallest P-value.
A p-value is a statistical measurement used to validate a hypothesis against observed data. A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true. The lower the p-value, the greater the statistical significance of the observed difference.
Know more about P-value here:
https://brainly.com/question/13786078
#SPJ11
what is the formula for calculating the coefficient of determination
The coefficient of determination, also known as R-squared, is a statistical measure that represents the proportion of the variance in a dependent variable that is predictable from an independent variable or variables. It is used to evaluate the goodness of fit of a regression model. The formula for calculating the coefficient of determination is:
R-squared = 1 - (SSres / SStot)
where SSres is the sum of squares of residuals and SStot is the total sum of squares.
The sum of squares of residuals is calculated by subtracting each predicted value from its corresponding actual value, squaring the difference, and adding up all the squared differences. The total sum of squares is calculated by subtracting the mean of the dependent variable from each actual value, squaring the difference, and adding up all the squared differences.
The coefficient of determination ranges from 0 to 1, with 0 indicating that the model does not explain any variability in the dependent variable and 1 indicating that the model explains all the variability in the dependent variable. A higher R-squared value indicates a better fit between the regression model and the data.
It is important to note that R-squared should not be used as the sole criterion for evaluating a regression model. Other factors such as statistical significance, residual plots, and out-of-sample prediction accuracy should also be considered.
To know more about coefficient of determination refer here:
https://brainly.com/question/31891074#
#SPJ11
Malcom has $638.54 in his checking account he must maintain a $500 balance to avoid a fee he wrote a check for $159.50 today write and solve an inequality to solve for the least amount of money he needs to avoid a fee
Answer:
$20.96
Step-by-step explanation:
He has $638.54 in his account and writes a check for $159.50. The amount of money he needs to stay at or above $500 is denoted by x.
638.54 - 159.50 + x >= 500
After writing a check, Malcom has $479.04 left in his account, which is below his cutoff.
479.04 + x >= 500
He must add at least x amount of dollars to his account to avoid a fee.
x >= 20.96
In order to avoid a fee, Malcom must add a minimum of $20.96 to his account.
Find a function r(t) that describes the line segment from P(2,7,3) to Q(3,1,1). A. r(t)=⟨2−t,7+6t,3+2t⟩;0≤t≤1 B. r(t)=⟨2+t,7−6t,3−2t⟩;0≤t≤1 C. r(t)=⟨2+t,7−6t,3−2t⟩;1≤t≤2 D. r(t)=⟨2−t,7+6t,3+2t⟩;1≤t≤2
The correct function that describes the line segment from P(2,7,3) to Q(3,1,1) is r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩; 0 ≤ t ≤ 1.
The function that describes the line segment from point P(2,7,3) to Q(3,1,1), we can use the parametric form of a line. The general form of a line equation is r(t) = ⟨x₀ + at, y₀ + bt, z₀ + ct⟩, where (x₀, y₀, z₀) is a point on the line and (a, b, c) are direction ratios.
1. First, we find the direction ratios by subtracting the coordinates of P from Q:
a = 3 - 2 = 1
b = 1 - 7 = -6
c = 1 - 3 = -2
2. Next, we substitute the point P(2,7,3) into the line equation and simplify:
r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩
3. The parameter t represents the distance along the line segment. Since we want to describe the segment from P to Q, we need t to vary from 0 to 1, ensuring that we cover the entire segment.
4. Comparing the obtained equation with the given options, we find that the correct function is r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩; 0 ≤ t ≤ 1.
Therefore, option A, r(t) = ⟨2 - t, 7 + 6t, 3 + 2t⟩; 0 ≤ t ≤ 1, is the correct answer.
Learn more about function : brainly.com/question/28278690
#SPJ11
for f(x) = 8x - 5, determine f^-1(1)
Answer:
Step-by-step explanation:
f^-1(x)=8(1/x)-5
f^-1(1)=8(1/1)-5=3
Answer:
\(\frac{3}{4}\)
Step-by-step explanation:
PLEASE HURRY ILL GIVE BRAINLIEST FOR FIRST ANSWER
What is the value of x?
6.75 + StartFraction 3 Over 8 EndFraction x = 13 and one-fourth
a. 2 and StartFraction 7 Over 16 EndFraction
b. 17 and one-third
c. 18 and two-thirds
d. 53 and one-third
Answer:
(b) 17 1/3
Step-by-step explanation:
mixed number
A number is written as a whole number and a fraction
Need a little help :,)
Answer:
A a. 25 minutes
Step-by-step explanation:
Let x = time in minutes.
Aquarium I contains y water at time x.
y = 4.6 + 1.2x
Aquarium II contains y water at time x,
y = 54.6 - 0.8x
We want the amounts of water to be equal, so we set the right parts of the equations equal and solve for x, the time in minutes.
4.6 + 1.2x = 54.6 - 0.8x
Subtract 4.6 from both sides.
Add 0.8x to both sides.
2x = 50
Divide both sides by 2.
x = 25
What is the measure of the missing angle in this triangle?
35°
60°
155°
25°
Answer:
25 is the answer.
Step-by-step explanation:
Hope this helps!!
in a standard 52-card deck of plyaing cards, each card has one of four suits: spade, heart, club, or diamond
In a standard 52-card deck of playing cards, each card is assigned one of four suits: spade, heart, club, or diamond. These suits are represented by symbols that are printed on the cards.
The deck consists of 13 cards for each suit. Within each suit, there are four face cards (king, queen, and jack) and nine numbered cards (from 2 to 10). Additionally, each suit has an Ace card, which can be counted as either a high or low card depending on the game being played. To summarize, a standard 52-card deck of playing cards consists of four suits (spade, heart, club, and diamond), each containing 13 cards. This provides a total of 52 cards in the deck. A standard 52-card deck of playing cards consists of four suits: spade, heart, club, and diamond. Each suit has 13 cards, including four face cards and nine numbered cards. In a standard 52-card deck of playing cards, the suits are spade, heart, club, and diamond. Each suit has its own symbol and color. Spades and clubs are black suits, represented by a ♠ and ♣ symbol, respectively. Hearts and diamonds are red suits, represented by a ♥ and ♦ symbol, respectively. Each suit contains 13 cards, making a total of 52 cards in the deck. Within each suit, there are four face cards: the king, queen, and jack. These cards often have additional designs or symbols, depending on the deck's style. In addition to the face cards, each suit has nine numbered cards, ranging from 2 to 10. Furthermore, each suit has an Ace card, which is considered the highest-ranking card in many card games. However, the Ace can also be used as a low card in some games, depending on the rules.
In a standard 52-card deck of playing cards, there are four suits: spade, heart, club, and diamond. Each suit contains 13 cards, including four face cards, nine numbered cards, and an Ace card. The deck is used for various card games, and the suits are represented by different symbols and colors.
To learn more about 52-card deck visit:
brainly.com/question/30756836
#SPJ11
How wide is the chasm between what men and women earn in the workplace? According to a 2015 analysis from a national women's group, women lose $435,049 over the course of a career because of the pay gap. The bar graph to the right shows the average earnings in the United States for men and women at ages and. This exercise involves the graphs of models for the data shown in the rectangular coordinate system to the right. Complete parts (a) through (c) below
The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women.
In the United States, there exists a substantial wage gap between men and women. According to a 2015 analysis by a national women's group, women lose $435,049 over the course of their careers due to the pay gap. The average earnings of men and women are shown in the bar graph to the right at various ages. The disparity between men's and women's earnings in the workplace is a critical problem.
According to the graph above, the average earnings for women and men vary widely as they age. The pay gap at the start of a woman's working career is modest, but it grows rapidly and becomes much more substantial as she ages and advances through her career. As depicted in the graph, the average earnings for men and women are reasonably similar at the beginning of their working careers, with both sexes earning an average of roughly $20,000 at age 20.
The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women. The chasm between what men and women earn in the workplace, according to the data provided, is considerable.
Learn more about substantial wage gap from:
brainly.com/question/13717043
#SPJ4
The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women.
In the United States, there exists a substantial wage gap between men and women. According to a 2015 analysis by a national women's group, women lose $435,049 over the course of their careers due to the pay gap. The average earnings of men and women are shown in the bar graph to the right at various ages. The disparity between men's and women's earnings in the workplace is a critical problem.
According to the graph above, the average earnings for women and men vary widely as they age. The pay gap at the start of a woman's working career is modest, but it grows rapidly and becomes much more substantial as she ages and advances through her career. As depicted in the graph, the average earnings for men and women are reasonably similar at the beginning of their working careers, with both sexes earning an average of roughly $20,000 at age 20.
The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women. The chasm between what men and women earn in the workplace, according to the data provided, is considerable.
Learn more about substantial wage gap from:
brainly.com/question/13717043
#SPJ11
How wide is the chasm between what men and women earn in the workplace? According to a 2015 analysis from a national women's group, women lose 5435,049 over the course of a career because of the pay gap. The bar graph to the right shows the average carnings in the United States for men and women at ages 22 and 57 This exercise Involves the graphs of models for the data shown in the rectangular coordinate system to the right. Complete parts (6) through (c) below. Average Yearly Eamings in the US by Gender and Age 70 GO (COL) ಠ ಠ Average aty Earrings (51000) ကို နိုင် ငံ မှ 370 560. 550 TROPY 540 530 5200 00.21 $10 50 0 10 20 30 40 50 Years Age 22 10 Age Use the two points for men shown on the graph to find a function in the form M(x)= mx + b that models average yearly earnings for men x years after age 22 M(x)- (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed)
I get an automatic 100 just for completing the assignment and I’m failing right now and really stressed. Should I just guess and receive all hundreds or actually work it out, it’s due at 12 and I have four more assignments.
Answer:
Just try your best for all of it, but make sure for each question, you at least have an answer, so the assignmet would count as complete.
Step-by-step explanation:
Answer:
submit whatever you have, guess all of it to get it all done. if you have time you can go back and check
Step-by-step explanation:
What percent of 40 is 12?
O 30%
0 70%
0 20%
0 40%
Answer:
30
Step-by-step explanation:
12÷40×100
12×100÷40=30
A local nonprofit organization is selling popcorn to raise money for hurricane relief. The organization paid $4 per bag for the popcorn and sold it for $5 per bag. What was the percent markup on each bag of popcorn?
Alice went to the movie with 2 of her friends and spent $10.50. 30% of the total wad spent on movie snacks. Which proportion could be used to calculate the total amount that Alice spent on movie snacks?A. 30/100 = x/10.5B. 30/100 = 10.5/ xC. 10.5/100 = 30/xD. x/100 = 10.5/30
Alice spend a total of $10.50, and the 30% of total was spent on snacks.
So, if we call x the money spent on snacks we have that the ratio between x and total spent money is 30%:
\(\frac{x}{10.5}=\frac{30}{100}\)Write an absolute value inequality for the graph below GRAPH ADDED. Please reply with correct answer 1/3
The absolute value inequality for the graph is given as |x| < 4
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
The absolute value is given by:
|x - average| = distance to midpoint
From the graph:
x > -4 and x < 4
The midpoint is 0, hence Distance between -4 or 4 to midpoint (0) is 4
Average = (-4 + 4)/2 = 0
Hence:
|x - 0| = 4
|x| < 4
The absolute value inequality for the graph is given as |x| < 4
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
The temperature in Virginia fell
from 12.3°C to -4.7°c. What is
the difference between the two
temperatures?
Answer:
17
Step-by-step explanation:
you add the absolute values
Suppose you are learning about infants for a class and need to write a paper on one baby. From a list of births over the past year at a hospital, choose one baby at random. Which of the following events are mutually exclusive (disjoint)?
A. The child having blue eyes and weighing over 10 pounds.
B. The child having brown hair and being a girl.
C. The child being born on a Wednesday and on the weekend.
D. The child being a boy and being over 20 inches tall.
ANSWER IS C
Answer:
C
Step-by-step explanation:
Don't listen to those *other* answers, clearly the correct one is c
(kidding kidding xD)
Why is Triangle MAE congruent to Triangle TON
The most significant difference between the static and current electricity is that in static electricity the charges are at rest and they are accumulating on the surface of the insulator. Whereas in current electricity the electrons are moving inside the conductor.
Hope this helps I don't even know if your looking for this.
Solve the system of equations by graphing on your own paper. What is the y
coordinate of the solution?
= 2x-1
= -2x+5
Answer: The coordinate of the solution is (0.25,-0.5)
Step-by-step explanation:
the solution is (0.25,-0.5) because when you graph them on a graph, they both intercept at that point.
Write 41. 287 to 1 decimal place
What does 6 divided by 8 plus 8 equal?
Answer:
6 3/4
Step-by-step explanation:
6/8+6
6 6/8
You can simplify to 6 3/4
Answer:
8.75
Punishment?
What is the 44th term of the sequence specified by the following closed form and range of values of n? a_n =4/n (n=1,2,3,...) n Give your answer as an exact number or fraction.
The 44th term of the sequence specified by the closed form \(a_n = \frac{4}{n}\) for \(n = 1, 2, 3, \ldots\) is \(\frac{1}{11}\).
The sequence specified by the closed form \(a_n = \frac{4}{n}\) for \(n = 1, 2, 3, \ldots\) is a harmonic sequence. To find the 44th term of this sequence, we substitute \(n = 44\) into the formula:
\(a_{44} = \frac{4}{44}\)
To simplify this fraction, we can find the greatest common divisor (GCD) of 4 and 44, which is 4. Dividing both the numerator and denominator by 4, we get:
\(a_{44} = \frac{1}{11}\)
Therefore, the 44th term of the sequence is \(\frac{1}{11}\).
A harmonic sequence is a sequence of the form \(a_n = \frac{1}{n}\), where the terms are obtained by taking the reciprocal of positive integers. In this case, we have a modified harmonic sequence with a constant term of 4 in the numerator.
Each term of the sequence is the reciprocal of the corresponding positive integer. For example, the first term is \(a_1 = \frac{4}{1} = 4\), the second term is \(a_2 = \frac{4}{2} = 2\), and so on. The general pattern is that the value of the term decreases as \(n\) increases.
As \(n\) increases, the terms get closer and closer to zero, but they never actually reach zero. The sequence approaches zero as the values of \(n\) get larger, but it never reaches zero for any finite \(n\).
In this case, we specifically need to find the 44th term of the sequence. By substituting \(n = 44\) into the formula, we find that the 44th term is \(\frac{1}{11}\).
Therefore, the 44th term of the sequence specified by the closed form \(a_n = \frac{4}{n}\) for \(n = 1, 2, 3, \ldots\) is \(\frac{1}{11}\).
Learn more about sequence here
https://brainly.com/question/7882626
#SPJ11
What is the inverse of f(x)=2x^2+4x? Please show work.
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
\(\stackrel{f(x)}{y}~~ = ~~2x^2+4x\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^2+4y} \\\\\\ x=2(y^2+2y)\implies \cfrac{x}{2}=y^2+2y\impliedby \begin{array}{llll} \textit{now let's complete the square}\\ \textit{to make it a perfect square trinomial}\\ \textit{by using our good friend, Mr "0"} \end{array} \\\\\\ \cfrac{x}{2}=y^2+2y(+1^2-1^2)\implies \cfrac{x}{2}=y^2+2y+1-1\implies \cfrac{x}{2}=(y^2+2y+1)-1\)
\(\cfrac{x}{2}+1=(y^2+2y+1^2)\implies \cfrac{x}{2}+1=(y+1)^2\implies \sqrt{\cfrac{x}{2}+1}=y+1 \\\\\\ \sqrt{\cfrac{x+2}{2}}=y+1\implies \sqrt{\cfrac{x+2}{2}}-1=y~~ = ~~f^{-1}(x)\)
ronald lau, chief engineer at south dakota electronics, has to decide whether to build a new state-of-the-art processing facility. if the new facility works, the company could realize a profit of $200,000. if it fails, south dakota electronics could lose $190,000. at this time, lau estimates a 50% chance that the new process will fail. the other option is to build a pilot plant and then decide whether to build a complete facility. the pilot plant would cost $5,000 to build. lau estimates a 60% chance that the pilot plant will work. if the pilot plant works, there is a 75% probability that the complete plant, if it is built, will also work. if the pilot plant does not work, there is only a 30% chance that the complete project (if it is constructed) will work. lau faces a dilemma. by analyzing this problem, help lau to maximize his expected payoff. what is the best decision you recommend for lau and what is the expected payoff? write your answer in the space below
I recommend that Ronald Lau build the pilot plant first to maximize his expected payoff. The expected payoff for this decision is $55,000.
To help Ronald Lau maximize his expected payoff, we can use decision analysis to evaluate the potential outcomes and probabilities of each decision.
The first decision is whether to build the new facility directly or to build the pilot plant first and then decide whether to build the complete facility.
If the new facility is built directly, the expected payoff is $200,000 × 0.5 + (-$190,000) × 0.5 = $5,000.
If the pilot plant is built first, the expected payoff is:
$5,000 + $200,000 × 0.75 × 0.6 + (-$190,000) × 0.25 × 0.6 = $55,000
or
$5,000 + (-$190,000) × 0.75 × 0.4 + $200,000 × 0.25 × 0.4 = -$45,000
The best decision is to build the pilot plant first since this decision has a higher expected payoff of $55,000 compared to the expected payoff of $5,000 for building the new facility directly.
Learn more about the probability at
https://brainly.com/question/30034780?referrer=searchResults
#SPJ4
If the original quantity is 8 and the new quantity
is 2, what is the percent decrease?
If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
How did we figure this out?
For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:
\(\boxed{8-2=6}\\\boxed{6/2=3}\)
We are going to take that 25% and multiply it with 3 to get are final answer.
What is the missing number of 25 and 3?\(\boxed{25*3=75}\\\boxed{So,2=75}\)
Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
5(x−4)=15 please help me answer this problem im having a lot of troube
Answer:
=7
Step-by-step explanation:
12. A talented soccer player is expected to score 25 goals in a given soccer season.<
a) Find an upper bound on the probability that he scores 30 goals or more during the season.<
b) If he has a standard deviation of 6.5 goals during the season, give a bound on the probability that he scores between 12 and 38 goals during the season.
Looking up the cumulative probability for z = -2.000, we find that it is approximately 0.0228. Looking up the cumulative probability for z = 2.000, we find that it is approximately 0.9772. Therefore, the bound on the probability that the player scores between 12 and 38 goals during the season is approximately 0.9772 - 0.0228 = 0.9544, or approximately 95.44%.
To solve this problem, we need to make certain assumptions about the distribution of the soccer player's goal-scoring ability. Let's assume that the player's goal-scoring follows a normal distribution.
a) To find an upper bound on the probability that the player scores 30 goals or more during the season, we can use the concept of z-scores. First, we need to calculate the z-score for the value 30 using the mean and standard deviation:
z = (x - μ) / σ
where:
x = 30 (the value we want to find the probability for)
μ = 25 (mean)
σ = 6.5 (standard deviation)
z = (30 - 25) / 6.5 ≈ 0.769
Next, we need to find the probability associated with this z-score using a standard normal distribution table or a calculator. The probability associated with a z-score of 0.769 is the probability of scoring 30 goals or more during the season.
Looking up the probability in a standard normal distribution table or using a calculator, we find that the probability associated with a z-score of 0.769 is approximately 0.2206.
Therefore, the upper bound on the probability that the player scores 30 goals or more during the season is approximately 0.2206.
b) To find a bound on the probability that the player scores between 12 and 38 goals during the season, we need to calculate the z-scores for both values.
For 12 goals:
z1 = (x1 - μ) / σ
= (12 - 25) / 6.5
≈ -2.000
For 38 goals:
z2 = (x2 - μ) / σ
= (38 - 25) / 6.5
≈ 2.000
Next, we need to find the cumulative probabilities associated with these z-scores using the standard normal distribution table or a calculator. The difference between these two probabilities will give us the bound on the probability of scoring between 12 and 38 goals during the season.
Looking up the cumulative probability for z = -2.000, we find that it is approximately 0.0228.
Looking up the cumulative probability for z = 2.000, we find that it is approximately 0.9772.
Therefore, the bound on the probability that the player scores between 12 and 38 goals during the season is approximately 0.9772 - 0.0228 = 0.9544, or approximately 95.44%.
Learn more about probability here:
https://brainly.com/question/31828911
#SPJ11
the serving size for the granola that ted likes to eat for breakfast is 3/4 cup. how many servings are there in a box that holds 13 cups? (what operation should be used here? solve the problem.)
With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.
Given that:
Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.
We need to know how many servings of 3/4 cup can be obtained from 13 cups.
now we need to divide 13 by 3/4
=13 ÷ 3/4
= 13 × 4/3
= 52/3
= 17\(\frac{1}{3}\)
With one third of a serving remaining, there are 17 servings total.
To learn more about divide:
https://brainly.com/question/15381501
#SPJ4
in the worst case, a linear search locates a value in an array of length n in ____ steps. group of answer choices o(log n) o(log n2) o(n2) o(n)
In the worst case, a linear search locates a value in an array of length n in O(n) steps.
A linear search is a basic search algorithm that sequentially checks each element in an array until it finds the target value or reaches the end of the array.
In the worst case scenario, the target value is not present in the array, and the linear search needs to iterate through all n elements of the array.
Since the linear search algorithm checks each element one by one, its time complexity is directly proportional to the size of the array. This means that as the array length (n) increases, the number of steps required by the linear search also increases linearly.
Therefore, the worst-case time complexity of a linear search is O(n), indicating that the number of steps grows in proportion to the size of the array.
It is important to note that other search algorithms, such as binary search, can achieve faster search times (e.g., O(log n)) in sorted arrays.
To know more about linear click here
brainly.com/question/30444906
#SPJ11
You are given the following information obtained from a random sample of 6 observations. Assume the population has a normal distribution. 14 20 21 16 18 19 a. What is the point estimate of u? b. Construct an 80% confidence interval for u. Construct a 98% confidence interval for u. d. Discuss why the 80% and 98% confidence intervals are different.
A higher confidence level is associated with a wider confidence interval.
a. The point estimate of µ = (14 + 20 + 21 + 16 + 18 + 19) / 6 = 108 / 6 = 18.
b. For 80% confidence interval for µ, the confidence coefficient is 1 - α = 0.8, so α = 0.2 / 2 = 0.1. From the z-table, we can find the corresponding value of z to be 1.28. The confidence interval can be calculated as follows:
Upper Bound: µ + z*σ / √n = 18 + (1.28)(2.3) / √6 = 21.35
Lower Bound: µ - z*σ / √n = 18 - (1.28)(2.3) / √6 = 14.65
The 80% confidence interval is (14.65, 21.35). For 98% confidence interval for µ, the confidence coefficient is 1 - α = 0.98, so α = 0.01. From the z-table, we can find the corresponding value of z to be 2.33. The confidence interval can be calculated as follows:
Upper Bound: µ + z*σ / √n = 18 + (2.33)(2.3) / √6 = 23.88
Lower Bound: µ - z*σ / √n = 18 - (2.33)(2.3) / √6 = 12.12
The 98% confidence interval is (12.12, 23.88). The 80% and 98% confidence intervals are different because as we move to higher confidence levels, the z-values become larger, which in turn causes the confidence intervals to become wider. Therefore, a higher confidence level is associated with a wider confidence interval.
To learn more about confidence interval refer :
https://brainly.com/question/24131141
#SPJ11