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's in this file?
To determine whether females appear to exhibit more variability than males in the length of time shopping in this mall, we can conduct a hypothesis test for comparing the variances of two independent samples.
Here are the steps to perform this test:
Step 1: State the null and alternative hypotheses:
Null hypothesis (H0): The variances of females and males are equal.
Alternative hypothesis (H1): The variance of females is greater than the variance of males.
Step 2: Select the significance level (α): In this case, the level of significance is given as 0.025, which means we will reject the null hypothesis if the obtained p-value is less than 0.025.
Step 3: Calculate the test statistic:
We will use the F-test statistic to compare the variances of the two samples. The formula for the F-test statistic is:
F = (S1^2 / S2^2)
Where S1^2 is the sample variance of females and S2^2 is the sample variance of males.
Step 4: Find the p-value:
The p-value can be obtained using a statistical software or Excel. By comparing the obtained F-test statistic to the F-distribution with (n1-1) degrees of freedom for females and (n2-1) degrees of freedom for males, we can determine the p-value.
Step 5: Make a decision:
If the obtained p-value is less than the chosen significance level (α), we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.
In conclusion, you would need to perform the F-test on the given data to compare the variances of the lengths of time shopping for females and males in order to determine if females appear to exhibit more variability.