Question

In Chapter 16 of the textbook we presented a case study that is associated with an attempt to develop a measure of physical ability. The data of this case study is saved in a file by the name "job.csv". Consider the following R code

> summary(job)
grip arm ratings sims
Min. : 29.0 Min. : 19.00 Min. :21.60 Min. :-4.1700
1st Qu.: 94.0 1st Qu.: 64.50 1st Qu.:34.80 1st Qu.:-0.9650
Median :111.0 Median : 81.50 Median :41.30 Median : 0.1600
Mean :110.2 Mean : 78.75 Mean :41.01 Mean : 0.2018
3rd Qu.:124.5 3rd Qu.: 94.00 3rd Qu.:47.70 3rd Qu.: 1.0700
Max. :189.0 Max. :132.00 Max. :57.20 Max. : 5.1700
> t.test(job$arm,mu=75)

One Sample t-test

data: job$arm
t = 2.1548, df = 146, p-value = 0.03282
alternative hypothesis: true mean is not equal to 75
95 percent confidence interval:
75.31075 82.19265
sample estimates:
mean of x
78.7517

The null hypothesis that states that the expectation of the variable "arm" is equal to 75 is:

Select one:

a. Not rejected with a significance level of 5%.

b. Rejected with a significance level of 5%, but not with a significance level of 1%.

c. Rejected with a significance level of 1%, but not with a significance level of 0.1%.

d. Rejected with a significance level of 0.1%

Answer 1

Here in this scenario the one sample t test is performed as above to test the claim that,

Claim : True mean is not equal to 75 .

Above claim is test by using one sample t test based on given sample information mean = 78.7571, n= 147.

From the given data test Statistic is 2.1548 from the test Statistic

p value= 2* P (ltl < 2.1548)

P-value = 0.03282.

Decesion Rule : Reject null Ho hypothesis if P-value is less than significance level (alpha). Other wise fail to Reject null hypothesis.

In our example if we take alpha at 0.05 then,

P-value = 0.03282 < alpha = 0.05 so we Reject Ho null hypothesis at 5% level of significance.

If we take Alpha at 0.01 then p value is greater than alpha 0.01 . So we fail to Reject null hypothesis.

So Option b) Reject at 5% level of significance, but not at 1% level of significance. Is correct decision.

Other options are incorrect.

Thank you.