Question

A state Department of Transportation claims that the mean wait time for various services at its different location is more than 6 minutes. A random sample of 16 services at different locations has a mean wait time of 9.5 minutes and a standard deviation of 7.3 minutes. At α=0.05, can the department’s claim be supported?a. No, since p of 0.037 is less than 0.05, fail to reject the null. Claim is alternative, so is not supportedb. Yes, since p of 0.037 is less than 0.05, reject the null. Claim is alternative, so is supportedc. No, since p of 0.037 is less than 0.05, reject the null. Claim is null, so is not supportedd. Yes, since p of 0.037 is less than 0.05, fail to reject the null. Claim is null, so is supported

Answer 1

Yes, since p of 0.037 is less than 0.05, reject the null. Claim is alternative, so is supported

Explanation:

`\µ = 6`

Sample size = 16

S = 7.3

`\bar{x}=9.5`

Significance level ( ∝) =0.05

`H_(0)` : µ = 6

`H_(a)` : µ > 6

The sample size n < 30 and the standard population deviation is uncertain, we will be using one t-test

Test Statistic :

`t=\bar{X}-\mu / s`

`t=(9.5-6)/(7.3 / √(16))=1.9178`

Finding the p value,

P value = 0.0371