You are considering moving to Richmond Hill and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 100 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes. A) $\mathrm { H } _ { 0 }$ : ? = 25 $\mathrm { H } _ { \mathrm { A } }$ : ? 25 C) $\mathrm { H } _ { 0 }$ : ? = 29 $\mathrm { H } _ { \mathrm { A } }$ : ? 29

Question

You are considering moving to Richmond Hill and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 100 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes. A) $\mathrm { H } _ { 0 }$ : ? = 25 $\mathrm { H } _ { \mathrm { A } }$ : ? < 25 B) $\mathrm { H } _ { 0 }$ : ? = 25 $\mathrm { H } _ { \mathrm { A } }$ : ? > 25 C) $\mathrm { H } _ { 0 }$ : ? = 29 $\mathrm { H } _ { \mathrm { A } }$ : ? < 29 D) $\mathrm { H } _ { 0 }$ : ? = 25 $\mathrm { H } _ { \mathrm { A } }$ : ? ? 25 E) $\mathrm { H } _ { 0 }$ : ? = 29 $\mathrm { H } _ { \mathrm { A } }$ : ? > 29

Quizplus · Accepted Answer

The null hypothesis (H0) is that the average one-way commute time to downtown Toronto is equal to or less than 25 minutes. The alternative hypothesis (Ha) is that the average one-way commute time to downtown Toronto is greater than 25 minutes.
Since the sample size (100) is large and the population standard deviation is unknown, we can use a one-sample t-test. We can calculate the t-statistic as:
t = (x̄ - μ) / (s/√n) = (29 - 25) / (7/√100) = 4
Using a significance level of 0.05 and degrees of freedom (df) = n - 1 = 99, the critical t-value for a one-tailed test is 1.660. Since the calculated t-value (4) is greater than the critical t-value (1.660), we reject the null hypothesis and conclude that the average one-way commute time from Richmond Hill to downtown Toronto exceeds 25 minutes. This is represented by the choice B, which states that the average commute time is greater than 25 minutes.

You Are Considering Moving to Richmond Hill and Are Concerned H0\mathrm { H } _ { 0 }H0​

You Are Considering Moving to Richmond Hill and Are Concerned $\mathrm { H } _ { 0 }$