Each person in random sample of 247 male and 253 female working adults living in Calgary, Canada was asked how long, in minutes, his or her typical daily commute was. use the accompanying summary statistics and an appropriate hypothesis test to determine if there is convincing evidence that the mean commute times for male and female working Calgary residents differ. Use a significance level of alpha=.05
males females
sample xbar s sample size xbar s
247 , 29.6, 24.3 - 253, 27.3,24.0
Follow the process indicated in your later post.
To determine if there is convincing evidence that the mean commute times for males and females differ, we can conduct a hypothesis test.
Step 1: Set up hypotheses:
- Null hypothesis (H0): The mean commute times for males and females are the same.
- Alternative hypothesis (Ha): The mean commute times for males and females are different.
Step 2: Determine the significance level:
The significance level (alpha) is given as 0.05.
Step 3: Compute the test statistic:
We can use the two-sample t-test to compare the means of two independent samples. The test statistic formula is:
t = (xbar1 - xbar2) / sqrt((s1^2 / n1) + (s2^2 / n2))
Where:
- xbar1 and xbar2 are the sample means (29.6 for males and 27.3 for females).
- s1 and s2 are the sample standard deviations (24.3 for males and 24.0 for females).
- n1 and n2 are the sample sizes (247 for males and 253 for females).
Plugging in the values:
t = (29.6 - 27.3) / sqrt((24.3^2 / 247) + (24.0^2 / 253))
Step 4: Calculate the p-value:
Using the t-distribution with degrees of freedom given by (n1 - 1) + (n2 - 1), we can calculate the p-value associated with the test statistic.
Step 5: Make a decision:
Compare the p-value to the significance level. If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 6: Interpret the results:
If we reject the null hypothesis, it means there is convincing evidence to suggest that the mean commute times for males and females in Calgary, Canada, are different. If we fail to reject the null hypothesis, there is not enough evidence to support a difference in mean commute times.
Note: The actual calculation of the t-statistic and the p-value will require a statistical software or calculator.