Question

Conduct a hypothesis test. Perform each of the following steps:

A) State the hypotheses and identify the claim

B) Find the critical value(s)

C) Compute the test value

D) Make the decision

E) Summarize the results

A survey found that the average commute time to work is 25.4 minutes. A researcher feels that the commute time in her city is longer. She randomly selects 25 commuters and finds the average time is 26.7 with a standard deviation of 5.3. Is the researcher’s claim correct at ? The variable is normally distributed.

Answer 1

Solution :

= 25.4

= 26.7

s =5.3

n = 25

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 25.4

Ha : > 25.4

Test statistic = t

= ( - ) / s / n

= (26.7 - 25.4) / 5.3 / 2

= 1.263

p(t > 1.263) = 1-P (t< 1.263 ) = 0.1094

P-value = 0.1094

The researcher’s claim is correct .