Math Problem Solver

An experiment was conducted to determine whether giving candy to dining parties resulted in greater tips. The mean tip percentages and standard deviations are given in the accompanying table along with the sample sizes. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b).

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Part 1

mu

n

x overbar

s

No candy

mu 1

28

18.02

1.57

Two candies

mu 2

28

20.52

2.57

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Part 1

a. Use a 0.01 significance level to test the claim that giving candy does result in greater tips.

What are the null and alternative​ hypotheses?

A.

Upper H 0​: mu 1equalsmu 2

Upper H 1​: mu 1greater thanmu 2

B.

Upper H 0​: mu 1equalsmu 2

Upper H 1​: mu 1less thanmu 2

Your answer is correct.C.

Upper H 0​: mu 1equalsmu 2

Upper H 1​: mu 1not equalsmu 2

D.

Upper H 0​: mu 1not equalsmu 2

Upper H 1​: mu 1less thanmu 2

Part 2

The test​ statistic, t, is

negative 4.39. ​(Round to two decimal places as​ needed.)

Part 3

The​ P-value is

0.000. ​(Round to three decimal places as​ needed.)

Part 4

State the conclusion for the test.

A.

Fail to reject the null hypothesis. There is sufficient evidence to support the claim that giving candy does result in greater tips.

B.

Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that giving candy does result in greater tips.

C.

Reject the null hypothesis. There is not sufficient evidence to support the claim that giving candy does result in greater tips.

D.

Reject the null hypothesis. There is sufficient evidence to support the claim that giving candy does result in greater tips.

Your answer is correct.

Part 5

b. Construct the confidence interval suitable for testing the claim in part​ (a).

enter your response hereless thanmu 1 minus mu 2less than

enter your response here

​(Round to two decimal places as​ needed.)