Question

We are interested in how long on average it takes Deadpool to grow back a leg. A simple random sample of 25 occasions results in an average of 62 minutes before Deadpool's leg grows back. Assume that the standard deviation of all grow-back-times is 10 minutes.

Vanessa claims that average, it takes Deadpool 65 minutes to grow back a leg. Do we have evidence that she's exaggerating the truth at each of the following levels?
The associated p-value for this hypothesis test is ( )? (Answers to four places after the decimal.)

(a) At the 13% level (yes or no?)

(b) At the 10% level (yes or no?)

(c)At the 7% level (yes or no?)

(d)At the 5% level (yes or no?)

(e)At the 3% level (yes or no?)

(f)At the 2% level (yes or no?)

(g)At the 1% level (yes or no?)

(h)At the 0.2% level (yes or no?)

(i)At the 0.1% level (yes or no?)

Answer 1

Define X=time to grow back, Assume X~N(m,SD=10)

To test H0: m=65 against H1: m is not equal to 65 .Then test is based on the Z statistic, defined by

,

Here Z=5*(62-65)/10=-1.5 so that |Z| is observed as 1.5.

Then

The associated p-value for this hypothesis test is .1336.

a) No as the null is supported

b) No as the null is supported

c-i) No. In all these cases p value is more than the nominal and hence we fail to reject the null. Thus there is no  exaggerating the truth .

For query in above, comment.