Question

2.     The dataset QuizPulse10 contains pulse rates collected from 10 students in a class lecture and then from the same ten students during a quiz. We might expect the mean pulse rate to increase under the stress of a quiz. Use the dataset to test at the 5% significance level whether there is evidence to support this claim.

a.     Perform the hypothesis test in Minitab.

b.    Make a decision and mathematically justify your decision

c.     Interpret the results.

student	quiz	lecture
1	75	73
2	52	53
3	52	47
4	80	88
5	56	55
6	90	70
7	76	61
8	71	75
9	70	61
10	66	78

Answer 1

Claim : To test whether or not the mean pulse rate increases under the stress of a quiz

Hypothesis :

  

Where ,

Right tailed test

By using minitab we can perform this test as

Put all the data in minitab worksheet then

Put all the data in minitab worksheet then

Click on STAT ----------> Basic statistics ----------> Paired t -------> Sample in column : First sample : ( Select the column of quiz data ) ------->Second sample : ( Select the column of Lecturedata ) ----->

Click on Options :

Confidence level : 95.0

Test Mean : 0.0

Alternative : Greater than

Click on OK -------->OK

we get the Minitab output as

Paired T-Test and CI: quiz, lecture

Paired T for quiz - lecture

N Mean StDev SE Mean
quiz 10 68.80 12.51 3.95
lecture 10 66.10 12.80 4.05
Difference 10 2.70 9.93 3.14

95% lower bound for mean difference: -3.06
T-Test of mean difference = 0 (vs > 0): T-Value = 0.86 P-Value = 0.206

We get the results as

Test statistics : t = 0.86

Pvalue = 0.206

Decision Rule : We Fail to Reject Ho

Conclusion : There is Insufficient evidence to conclude that mean pulse rate increases under the stress of a quiz .