Winnipeg Tribune claims that the time of travel from downtown to the University via the Pembina bus has an average of µ = 27 minutes. A student who normally takes this bus believes that µ is greater than 27 minutes. A sample of six ride-times taken to test the hypothesis of interest gave X = 27.5 minutes and a standard deviation s = 2.43 minutes, and the observations looked to have come from a symmetric distribution. The appropriate critical region and conclusion when testing at α= 0.05 are:

a. T* > 2.015; and we fail to reject H0.
b. T* > 2.571; and we fail to reject H0.
c. T* < 2.015; and we fail to reject H0.
d. T* < 2.571; and we fail to reject H0.
e. T* < 1.943; and we fail to reject H0.

To determine the appropriate critical region and conclusion when testing at α= 0.05, we can perform a hypothesis test using the t-distribution.

The null hypothesis, denoted as H0, assumes that the average travel time from downtown to the University via the Pembina bus is 27 minutes or less.

The alternative hypothesis, denoted as Ha, assumes that the average travel time is greater than 27 minutes.

We are given a sample of six ride-times with a sample mean (X) of 27.5 minutes and a standard deviation (s) of 2.43 minutes.

To calculate the test statistic, we use the formula:
t = (X - µ) / (s / sqrt(n))
where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:
t = (27.5 - 27) / (2.43 / sqrt(6))
t ≈ 1.943

To determine the critical value for a one-tailed test with a significance level of α = 0.05, we consult the t-distribution table (or use statistical software).

Looking up the critical value, we find that t* ≈ 2.571 (df = n-1 = 6-1 = 5).

Since our calculated test statistic (t ≈ 1.943) is less than the critical value (t* ≈ 2.571), it falls within the non-rejection region.

Therefore, the appropriate critical region and conclusion when testing at α = 0.05 is:
d. T* < 2.571; and we fail to reject H0.

This means that there is not enough evidence to support the claim that the average travel time from downtown to the University via the Pembina bus is greater than 27 minutes.