Use the following information for questions:
A bank official wants to assess if the average delays for two airlines are different.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 6 minutes delay with a standard deviation of 5 minutes. A random sample of 10 flights for Airline 2 shows an average of 12 minutes delay with a standard deviation of 5 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 = -2.68
B) t = -1.50
C) t = 1.50
D) t = 2.68

Question

Use the following information for questions:
 A bank official wants to assess if the average delays for two airlines are different.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 6 minutes delay with a standard deviation of 5 minutes. A random sample of 10 flights for Airline 2 shows an average of 12 minutes delay with a standard deviation of 5 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 = -2.68
B) t = -1.50
C) t = 1.50
D) t = 2.68

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 for groups 1 and 2, respectively. Plugging in the given values: $$t = \frac{6 - 12}{\sqrt{\frac{5^2}{10} + \frac{5^2}{10}}} = \frac{-6}{\sqrt{2.5 + 2.5}} = \frac{-6}{\sqrt{5}} = \frac{-6}{2.236} \approx -2.68.$$

Use the Following Information for Questions: a Bank Official µ1µ_1µ1​

Use the Following Information for Questions:
a Bank Official $µ_1$