A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Usea level of significance of 0.05.

Question

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Usea level of significance of 0.05.

Answer 1

Need mean and standard deviation of sample.

Answer 2

To conduct the test of hypothesis, we need to follow these steps:

Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1).
In this case, the null hypothesis would be:
H0: The average travel time of all the university's students is equal to 20 minutes.
And the alternative hypothesis would be:
H1: The average travel time of all the university's students differs from 20 minutes.

Step 2: Choose the appropriate statistical test.
Since we are comparing the population mean to a specific value and have a sample size greater than 30, we can use a Z-test.

Step 3: Determine the level of significance (α).
Given that the level of significance is 0.05, we set α = 0.05.

Step 4: Calculate the test statistic.
The test statistic for a Z-test is calculated using the formula:
Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
In this case, we need the sample mean, population mean, standard deviation, and sample size.

Step 5: Find the critical value.
Since we have a two-tailed test (looking for differences on both sides), we need to find the critical values for a Z-test based on a level of significance of 0.05. This can be done using a Z-table or calculator.

Step 6: Compare the test statistic to the critical value.
If the test statistic falls within the critical value range, we fail to reject the null hypothesis. If the test statistic falls outside the critical value range, we reject the null hypothesis.

Please provide the values for the sample mean, population mean, standard deviation, and sample size so we can proceed with the calculations.