In an analysis investigating the usefulness of pennies, the cents portions of 86 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 33.1 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.01 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts (a) through (e) below. Question content area bottom Part 1 a. Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: σ=28.866 cents H1: σ≠28.866 cents B. H0: σ≠28.866 cents H1: σ=28.866 cents C. H0: σ=28.866 cents H1: σ>28.866 cents D. H0: σ≥28.866 cents H1: σ<28.866 cents Part 2 b. Compute the test statistic. χ2=enter your response here (Round to three decimal places as needed.) Part 3 c. Find the P-value of the test statistic. The P-value of the test statistic is enter your response here. (Round to three decimal places as needed.) Part 4 d. State the conclusion. Do not reject H0. There is not is not is sufficient evidence to warrant rejection of the claim that the cents portion of credit card transactions has a standard deviation equal to 28.866 cents. Part 5 e. If the amounts from 0 cents to 99 cents are all equally likely, is the requirement of a normal distribution satisfied? If not, how does that affect the conclusion? A. Yes, because in that case the sampling distribution of standard deviations is approximately normally distributed, so the results of standard deviation hypothesis tests are reliable. B. No, because in that case the underlying population is not normally distributed, so the results of standard deviation hypothesis tests are not reliable. C. No, because in that case the underlying population is not normally distributed, but the central limit theorem indicates that the conclusion is still valid. D. Yes, because in that case the underlying population is normally distributed, so the results of standard deviation hypothesis tests are reliable. More

In an analysis investigating the usefulness of pennies, the cents portions of 86 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 33.1 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.01 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts (a) through (e) below. Question content area bottom Part 1 a. Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: σ=28.866 cents H1: σ≠28.866 cents B. H0: σ≠28.866 cents H1: σ=28.866 cents C. H0: σ=28.866 cents H1: σ>28.866 cents D. H0: σ≥28.866 cents H1: σ<28.866 cents Part 2 b. Compute the test statistic. χ2=enter your response here (Round to three decimal places as needed.) Part 3 c. Find the P-value of the test statistic. The P-value of the test statistic is enter your response here. (Round to three decimal places as needed.) Part 4 d. State the conclusion. Do not reject H0. There is not is not is sufficient evidence to warrant rejection of the claim that the cents portion of credit card transactions has a standard deviation equal to 28.866 cents. Part 5 e. If the amounts from 0 cents to 99 cents are all equally likely, is the requirement of a normal distribution satisfied? If not, how does that affect the conclusion? A. Yes, because in that case the sampling distribution of standard deviations is approximately normally distributed, so the results of standard deviation hypothesis tests are reliable. B. No, because in that case the underlying population is not normally distributed, so the results of standard deviation hypothesis tests are not reliable. C. No, because in that case the underlying population is not normally distributed, but the central limit theorem indicates that the conclusion is still valid. D. Yes, because in that case the underlying population is normally distributed, so the results of standard deviation hypothesis tests are reliable. More

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

In an analysis investigating the usefulness of pennies, the cents portions of 86 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 33.1 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.01 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts (a) through (e) below.
Question content area bottom
Part 1
a. Identify the null and alternative hypotheses. Choose the correct answer below.
A.
H0: σ=28.866 cents
H1: σ≠28.866 cents
B.
H0: σ≠28.866 cents
H1: σ=28.866 cents
C.
H0: σ=28.866 cents
H1: σ>28.866 cents
D.
H0: σ≥28.866 cents
H1: σ<28.866 cents
Part 2
b. Compute the test statistic.
χ2=enter your response here
(Round to three decimal places as needed.)
Part 3
c. Find the P-value of the test statistic.
The P-value of the test statistic is enter your response here.
(Round to three decimal places as needed.)
Part 4
d. State the conclusion.
Do not reject
H0. There
is not
is not
is
sufficient evidence to warrant rejection of the claim that the cents portion of credit card transactions has a standard deviation equal to 28.866 cents.
Part 5
e. If the amounts from 0 cents to 99 cents are all equally likely, is the requirement of a normal distribution satisfied? If not, how does that affect the conclusion?
A.
Yes, because in that case the sampling distribution of standard deviations is approximately normally distributed, so the results of standard deviation hypothesis tests are reliable.
B.
No, because in that case the underlying population is not normally distributed, so the results of standard deviation hypothesis tests are not reliable.
C.
No, because in that case the underlying population is not normally distributed, but the central limit theorem indicates that the conclusion is still valid.
D.
Yes, because in that case the underlying population is normally distributed, so the results of standard deviation hypothesis tests are reliable.
More

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution