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.
-What is the value of the test statistic?
A) t =-1.80
B) t =-102.00
C) t =-2.33
D) None of the above

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.
-What is the value of the test statistic?
A) t =-1.80
B) t =-102.00
C) t =-2.33
D) None of the above

Quizplus · Accepted Answer

The test statistic for comparing two means with unequal variances (Welch's t-test) is calculated using the formula: $t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$, where $\bar{x}_1$ and $\bar{x}_2$ are the sample means, $s_1^2$ and $s_2^2$ are the sample variances, and $n_1$ and $n_2$ are the sample sizes. Plugging in the given values: $t = \frac{9.5 - 12.63}{\sqrt{\frac{3^2}{10} + \frac{3^2}{10}}} = \frac{-3.13}{\sqrt{\frac{9}{10} + \frac{9}{10}}} = \frac{-3.13}{\sqrt{1.8}} = \frac{-3.13}{1.3416} \approx -2.33$.

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

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