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 7.6 minutes. At α=0.05, can the department’s claim be supported assuming the population is normally distributed?

No, since p of 0.043 is greater than 0.05, reject the null. Claim is null, so is not supported

No, since p of 0.043 is greater than 0.05, fail to reject the null. Claim is alternative, so is not supported

Yes, since p of 0.043 is less than 0.05, reject the null. Claim is alternative, so is supported

Yes, since p of 0.043 is greater than 0.05, fail to reject the null. Claim is null, so is supported

Answer 1

H₀: = 6

H₁: > 6

The test statistic t = ()/(s/)

                             = (9.5 - 6)/(7.6/)

                             = 1.84

P-value = P(T > 1.84)

            = 1 - P(T < 1.84)

            = 1 - 0.9572

            = 0.0428 = 0.043

Since the P-value is less than the significance level(0.043 < 0.05), so we should reject the null hypothesis.

So at 0.05 significance level there is sufficient evidence to support the claim that the mean wait time for various services at its different location is more than 6 minutes.

Option - C) Yes, since p of 0.043 is less than 0.05, reject null. Claim is alternative, so is supported.