A company wants to determine whether its consumer product ratings (0−10) have changed from last year to this year. The table below shows the company's product ratings from eight consumers for last year and this year. At α=0.05, is there enough evidence to conclude that the ratings have changed? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Consumer 1 2 3 4 5 6 7 8 Rating (last year) 5 8 6 4 6 8 7 5 Rating (this year) 2 5 5 4 4 6 8 4 (b) Let μd be the hypothesized mean of the ratings last year minus the ratings this year. State H0 and Ha. Choose the correct answer below. A. H0: μd≤0 Ha: μd>0 B. H0: μd≥d Ha: μd (c) Calculate d and sd. d=__ (Type an integer or a decimal.) Calculate sd. sd=_ (Type an integer or a decimal. Round to three decimal places as needed.) (d) Use the t-test to find the standardized test statistic t. t=___ (Type an integer or a decimal. Round to three decimal places as needed.) (e) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. (a) Reject the null hypothesis. (b) Fail to reject the null hypothesis. (f) Interpret the decision in the context of the original claim. Choose the correct answer below.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A company wants to determine whether its consumer product ratings

(0−10)

have changed from last year to this year. The table below shows the company's product ratings from eight consumers for last year and this year. At

α=0.05,

is there enough evidence to conclude that the ratings have changed? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f).

Consumer	1	2	3	4	5	6	7	8
Rating (last year)	5	8	6	4	6	8	7	5
Rating (this year)	2	5	5	4	4	6	8	4

(b) Let

μd

be the hypothesized mean of the ratings last year minus the ratings this year. State

and

Ha.

Choose the correct answer below.

H0:

μd≤0

Ha:

μd>0

H0:

μd≥d

Ha:

μd<d

H0:

μd=0

Ha:

μd≠0

H0:

μd≠0

Ha:

μd=0

H0:

μd≥0

Ha:

μd<0

H0:

μd≤d

Ha:

μd>

d=____

(Type an integer or a decimal.)

Calculate

sd.

sd=___

(Type an integer or a decimal. Round to three decimal places

as needed.)

(d) Use the t-test to find the standardized test statistic t.

t=___

(Type an integer or a decimal. Round to three decimal places as needed.)

(e) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.

(a) Reject the null hypothesis.

(b) Fail to reject the null hypothesis.

(f) Interpret the decision in the context of the original claim. Choose the correct answer below.

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.

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