Question

A delivery company claims that the mean time it takes to deliver frozen food between two particular cities is 4 hours. A consumer advocacy group wishes to show at the 5% level that the mean time is greater than 4 hours. A random sample of 50 deliveries yielded a sample mean of 4.2 hours with a standard deviation
of 0.5 hours.

1. Set up the null and alternative hypotheses.
2. Compute the test statistic.
3. State the p-value for the test.
4. State the decision and conclusion of the test in context.

Answer 1

Solution :

= 4

=4.2

S =0.5

n = 50

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :    = 4

H_a : > 4

Test statistic = t

= ( - ) / S / n

= (4.2-4) / 0.5 / 50

= 2.828

Test statistic = t = 2.828

P-value =0.0034

= 0.05  

P-value <

0.0034 < 0.05

Reject the null hypothesis .

There is sufficient evidence to claim that the population mean μ is greater than 4, at the 0.05 significance level.