Question

Settings Accessibility + On-Screen Keyboard + About +

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	Copy to Clipboard + Open in Excel +
Rating left parenthesis last year right parenthesisRating (last year)	55	66	55	22	99	66	66	55
Rating (this year)	22	77	33	11	55	55	55	44

(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

The claim is "The product ratings have

▼

decreased

not changed

changed

increased

from last year to this year."Let

mu Subscript dμd

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

Upper H 0H0

and

Upper H Subscript aHa.

Choose the correct answer below.

A.

Upper H 0H0 :

mu Subscript dμdgreater than or equals≥0

Upper H Subscript aHa :

mu Subscript dμdless than<0

B.

Upper H 0H0 :

mu Subscript dμdless than or equals≤0

Upper H Subscript aHa :

mu Subscript dμdgreater than>0

C.

Upper H 0H0 :

mu Subscript dμdnot equals≠0

Upper H Subscript aHa :

mu Subscript dμdequals=0

D.

Upper H 0H0 :

mu Subscript dμdless than or equals≤d overbard

Upper H Subscript aHa :

mu Subscript dμdgreater than>d overbard

E.

Upper H 0H0 :

mu Subscript dμdequals=0

Upper H Subscript aHa :

mu Subscript dμdnot equals≠0

F.

Upper H 0H0 :

mu Subscript dμdgreater than or equals≥d overbard

Upper H Subscript aHa :

mu Subscript dμdless than<d overbard

(b) Find the critical value(s) and identify the rejection region(s).

t 0t0equals=nothing

(Use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as needed.)

Identify the rejection region. Choose the correct answer below.

A.

tgreater than>1.895

B.

tless than<minus−2.365

C.

tless than<minus− 2.365,

tgreater than>2.365

D.

tless than<minus− 1.895,

tgreater than>1.895

(c) Calculate

d overbard

and

s Subscript dsd.

d overbardequals=nothing

(Type an integer or a decimal.)

Calculate

s Subscript dsd.

s Subscript dsdequals=nothing

(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.

tequals=nothing

(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.

RejectReject

the null hypothesis.

Fail to rejectFail to reject

the null hypothesis.

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

A.

At the 5% significance level, there

isis

enough evidence to support the claim that the product ratings have changed from last year to this year.

B.

The sample was not large enough to make a conclusion.

C.

The product ratings have changed from last year to this year.

D.

At the 5% significance level, there

is notis not

enough evidence to support the claim that the product ratings have changed from last year to this year.

Answer 1

Answer: