Question

A company wants to determine whether its consumer product ratings

​(0minus−​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

alphaαequals=​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 left parenthesis last year right parenthesisRating (last year)	55	55	44	22	66	88	55	77
Rating​ (this year)	44	55	66	22	55	1010	88	99

Answer 1

In the above problem data are dependent in nature and sample size is 8 that is this is small sample problem

So we use the dependent t-test for the above question.

Ho : There is enough evidence to conclude that the ratings have changed

H1 : There is not enough evidence to conclude that the ratings have changed

We use the formula of t statistic is as below

Sr No.	A	B	d =A - B
1	55	44	11
2	55	55	0
3	44	66	-22
4	22	22	11
5	66	55	0
6	88	10	78
7	55	88	-33
8	77	99	-22
Total			= 23

​​​​​​​

This calculated value of t = 0.2359

Table value of t (=TINV(probability, degrees of freedom) in Excel then press Enter key)

=TINV(Probability, n - 1)

= TINV(0.05, 7)

= 2.3646

Table value of t = 2.3646

calculated value of t = 0.2359 < Table value of t = 2.3646

here we accept Ho

There is enough evidence to conclude that the ratings have changed.