Question

DMV claims that their average wait times are less than 15 minutes. A random sample of 10 people had a mean wait time of 13 minutes with a standard deviation of 3.5 minutes. Assuming wait times are normally distributed , test the claim at alpha=0.10 . Hint : One Mean, T-test.

Answer 1

Answer:

n=10, =15,

= 13, s= 3.5,

=0.10

a)

the null and alternative hypotheses is

Ho: 15
Ha: < 15

Calculte test statistic

t = -1.807

Test statistic: t = −1.807

calculate t critical values for left tailed test with =0.1 and df= n-1 = 10-1=9

using t table we get

Critical values are = −1.383

decision rule is

Reject Ho if t < −1.383

here ( t= −1.807) < −1.383

hence,

Reject the Null hypothesis (Ho).

Conclusion:
There is sufficient evidence to support the claim that the average wait times are less than 15 minutes.