The average length of a flight by regional airlines in the United States has been reported as 299 miles. If a simple random sample of 30 flights by regional airlines If The average length of a flight by regional airlines in the United States has been reported as 299 miles. If a simple random sample of 30 flights by regional airlines were to have ȭ = 413/6 miles and s= 42.8 miles, would this tend to cast doubt on the reported average of 299 miles? Use a two-tail test and the 0.05 level of significance in arriving at your answer

Question

The average length of a flight by regional airlines in the United States has been reported as 299 miles. If a simple random sample of 30 flights by regional airlines If The average length of a flight by regional airlines in the United States has been reported as 299 miles. If a simple random sample of 30 flights by regional airlines were to have ȭ = 413/6 miles and s= 42.8 miles, would this tend to cast doubt on the reported average of 299 miles? Use a two-tail test and the 0.05 level of significance in arriving at your answer

Answer 1

To determine if the sample average of 413/6 miles and standard deviation of 42.8 miles casts doubt on the reported average of 299 miles, we can conduct a hypothesis test using a two-tailed test at the 0.05 level of significance.

Here are the steps to perform the hypothesis test:

Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1):
- Null hypothesis (H0): The reported average of 299 miles is correct.
- Alternative hypothesis (H1): The reported average of 299 miles is not correct.

Step 2: Choose the appropriate test statistic. In this case, we will use the t-test because we have a sample size of less than 30 and don't know the population standard deviation.

Step 3: Determine the critical value. Since we are using a two-tailed test with a significance level of 0.05, the critical value will be obtained from the t-distribution table. We will divide the significance level by 2 to account for the two tails. For a sample size of 30 and a significance level of 0.025 (0.05/2), the critical value is approximately 2.042 (look up the value in the t-distribution table with 29 degrees of freedom).

Step 4: Calculate the test statistic. The formula for the t-test is:
t = (x̄ - μ) / (s / √n)
where x̄ is the sample mean, μ is the population mean (reported average of 299 miles), s is the standard deviation, and n is the sample size.

Plugging in the values, we have:
t = ((413/6) - 299) / (42.8 / √30)

Step 5: Calculate the p-value. Using the t-distribution table and the degrees of freedom (29), we can find the p-value associated with the calculated t-value.

Step 6: Compare the p-value with the significance level (0.05). If the p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this case, you would need to calculate the t-value and p-value to determine whether the reported average of 299 miles is questionable based on the sample data.