Question

Randomly selected statistics students participated in an experiment to test their ability to determine when 1 minute (or 60 seconds) has passed. 44 students yielded a sample mean of 58.3 seconds. Assume that  = 9.5 seconds.

a) Use a 0.05 significance level to test the claim that the population mean is equal to 60 seconds.

Claim:   ---Select--- < > = ≠ ≤ ≥ 60

Ho:     ---Select--- < > = ≠ ≤ ≥ 60

H1:     ---Select--- < > = ≠ ≤ ≥ 60

b) What is the rejection result?

Do not reject the null hypothesis.Reject the null hypothesis.    Not enough information.

c) What is the conclusion?

There is not significant evidence that the perception of 1 minute differs from 60 seconds. The perception of elapsed time appears accurate.There is significant evidence that the perception of 1 minute differs from 60 seconds. The perception of elapsed time does not appear accurate.    There is not significant evidence that the perception of 1 minute differs from 60 seconds. The perception of elapsed time does not appear accurate.There is significant evidence that the perception of 1 minute differs from 60 seconds. The perception of elapsed time appears accurate.

Answer 1

Solution:

a)

Claim: = 60

H0: = 60

H1:   60

b)

The test statistic z is given by

z =

= (58.3 - 60) / (9.5/44)

= -1.19

in H1. So it is TWO tailed test.

p value = P(Z < -z) + P(Z > +z) = P(Z < -1.19) + P(Z> 1.19) = 0.117 + 0.117 = 0.234

p value is greater than significance levels 0.05 , 0.01 , 0.10

So ,

Do not reject the null hypothesis.

c)

There is not significant evidence that the perception of 1 minute differs from 60 seconds. The perception of elapsed time appears accurate