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 whether the reported average of 299 miles is questionable based on the provided sample, we can conduct a hypothesis test using a two-tail test with a significance level of 0.05.

Let's set up the null and alternative hypotheses:

Null hypothesis (H0): The population mean is equal to 299 miles.
Alternative hypothesis (H1): The population mean is not equal to 299 miles.

The given sample statistics are:
Sample mean (x̄) = 413/6 miles
Sample standard deviation (s) = 42.8 miles
Sample size (n) = 30 flights

To perform the hypothesis test, we will calculate the test statistic, which is the t-statistic in this case, using the formula:

t = (x̄ - μ) / (s / sqrt(n))

where μ is the hypothesized population mean (299 miles), x̄ is the sample mean, s is the sample standard deviation, and n is the sample size.

Let's calculate the t-statistic:

t = [(413/6) - 299] / (42.8 / sqrt(30))

Using a calculator or statistical software, we find that t ≈ 3.34.

Next, we need to determine the critical value(s) for the given significance level (0.05) and degrees of freedom (n - 1 = 30 - 1 = 29). Since this is a two-tail test, we split the significance level equally between the two tails, resulting in an alpha of 0.025 for each tail.

Looking up the critical value(s) in the t-distribution table or using a calculator, you will find that the critical t-values for a two-tail test with α = 0.025 and degrees of freedom = 29 are approximately ±2.045.

Since the calculated t-statistic (3.34) is greater than the critical t-value (2.045) in the right tail, we can reject the null hypothesis and conclude that there is evidence to suggest that the population mean is not equal to 299 miles.

In simpler terms, based on the provided sample data, the average flight length of 413/6 miles casts doubt on the reported average of 299 miles.