Use the following information for questions:
An airport official wants to assess if the flights from one airline (Airline 1) are less delayed than flights from another airline (Airline 2) . Let $µ_1$ = average delay for Airline 1 and $µ_2$ = average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 9.5 minutes delay with a standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a standard deviation of 3 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom.
-For a significance level of $\alpha$ = 0.05, are the results statistically significant?

Question

Use the following information for questions:
An airport official wants to assess if the flights from one airline (Airline 1) are less delayed than flights from another airline (Airline 2) . Let

µ_1

= average delay for Airline 1 and

µ_2

= average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 9.5 minutes delay with a standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a standard deviation of 3 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom.
-For a significance level of

\alpha

= 0.05, are the results statistically significant?

Quizplus · Accepted Answer

The hypothesis test compares two means with unequal variances, so a two-sample t-test is appropriate. Using the conservative estimate for degrees of freedom (df = min(n1-1, n2-1) = 9), and given the sample sizes, means, and standard deviations, the calculated t-value would indicate a significant difference if the p-value is less than 0.05. Given the context, the correct interpretation is that the results are statistically significant if the p-value is less than 0.05, indicating that the average delay for Airline 1 is significantly less than that for Airline 2 at the 0.05 significance level.

Use the Following Information for Questions: an Airport Official µ1µ_1µ1​

Use the Following Information for Questions:
an Airport Official $µ_1$