A researcher has observed independent samples of females and males, recording how long each person took to complete his or her shopping at a local mall. The respective times, in minutes, are listed in file. Using the 0.025 level of significance in a one-tail test, would females appear to exhibit more variability than males in the length of time shopping in this mall?
females males
26 33
35 40
75 50
63 32
36 28
71 39
54 32
68 33
37 31
48 36
42 26
43 37
73 38
55 21
47 39
71 48
27 38
56 36
37 59
25 59
88 53
42 59
33 35
66 38
45 24
53 28
46 45
74 28
58 23
51 15
58 61
48 31
48 17
42 55
55 31
50 55
61 37
28 36
41 20
58 48
What file? We can't help you unless we know the minutes listed in the file.
females males
26 33
35 40
75 50
63 32
36 28
71 39
54 32
68 33
37 31
48 36
42 26
43 37
73 38
55 21
47 39
71 48
27 38
56 36
37 59
25 59
88 53
42 59
33 35
66 38
45 24
53 28
46 45
74 28
58 23
51 15
58 61
48 31
48 17
42 55
55 31
50 55
61 37
28 36
41 20
58 48
Lina, either you reproduce the contents of the file so we can see the numbers, or you provide a link from where we can download the file for informtion. As Ms Sue said, it would not be possible to give further help if we don't see the data.
To determine if females exhibit more variability than males in the length of time shopping at the mall, we can perform a hypothesis test on the difference in variances between the two groups.
Here are the steps to perform the hypothesis test:
Step 1: State the null and alternative hypothesis.
Null hypothesis (H0): The variance of the time taken by females equals the variance of the time taken by males.
Alternative hypothesis (Ha): The variance of the time taken by females is greater than the variance of the time taken by males.
Step 2: Set the level of significance (α). In this case, the significance level is 0.025.
Step 3: Collect and organize the data. The recorded times for females and males are already provided.
Step 4: Calculate the sample variances for both groups. Use the formula for sample variance:
Sample Variance (s^2) = Σ(x - x̄)^2 / (n - 1)
where Σ represents the sum, x represents each individual data point, x̄ represents the mean, and n represents the sample size.
For the females:
Mean (x̄f) = (sum of female times) / (number of female times)
Sample Variance (s^2f) = Σ(female time - x̄f)^2 / (n - 1)
For the males:
Mean (x̄m) = (sum of male times) / (number of male times)
Sample Variance (s^2m) = Σ(male time - x̄m)^2 / (n - 1)
Step 5: Calculate the test statistic F using the formula:
F = s^2f / s^2m
Step 6: Look up the critical value from the F-distribution tables or use statistical software with the degrees of freedom (df1 = n - 1 for females and df2 = n - 1 for males) and the significance level (α = 0.025) to find the critical value.
Step 7: Compare the test statistic F with the critical value. If the test statistic F is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
If the null hypothesis is rejected, it would suggest that females exhibit more variability than males in the length of time shopping in this mall.
Please note that to perform the calculations and find the test statistic F and critical value, you will need to input the actual data values provided in the question into a statistical software or use appropriate spreadsheet functions.