Ernesto is a web developer who is looking to determine which of two types of advertisements are the most cost effective. He suspects that advertisements with animations generate more clicks than advertisements without animations but wants to confirm his intuition before he starts recommending advertisements with animations to his clients. Ernesto creates advertisements with animations for 12 different products and then creates advertisements without animations for those same products. Then he measures the click-through rate for those advertisements. The data are provided below (given as percentages of total visitors to the site who clicked on the advertisement). Assume that the conditions required for this hypothesis test are satisfied. Use a calculator to test the paired data, where α=0.01. Compute the sample differences d using d=Without−With. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the click rates of advertisements without animations and the click rates of advertisements with animations is less than 0?
Ernesto is a web developer who is looking to determine which of two types of advertisements are the most cost effective. He suspects that advertisements with animations generate more clicks than advertisements without animations but wants to confirm his intuition before he starts recommending advertisements with animations to his clients. Ernesto creates advertisements with animations for 12 different products and then creates advertisements without animations for those same products. Then he measures the click-through rate for those advertisements. The data are provided below (given as percentages of total visitors to the site who clicked on the advertisement). Assume that the conditions required for this hypothesis test are satisfied.
Use a calculator to test the paired data, where α=0.01. Compute the sample differences d using d=Without−With. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the click rates of advertisements without animations and the click rates of advertisements with animations is less than 0?
|
Pair |
Without Animations |
With Animations |
|
1 |
4.7 |
6.4 |
|
2 |
6.1 |
6.1 |
|
3 |
1.1 |
0.7 |
|
4 |
4.1 |
3.5 |
|
5 |
2.6 |
2 |
|
6 |
3.5 |
2.6 |
|
7 |
2.4 |
3.5 |
|
8 |
9.9 |
11.9 |
|
9 |
5.6 |
6.8 |
|
10 |
8.6 |
8.8 |
|
11 |
7.2 |
8.3 |
|
12 |
3.8 |
4.5 |
Select all that apply:
-
Reject the null hypothesis that the true mean difference between the click rates of advertisements without animations and the click rates of advertisements with animations is equal to 0.
-
Fail to reject the null hypothesis that the true mean difference between the click rates of advertisements without animations and the click rates of advertisements with animations is equal to 0.
-
Based on the results of the hypothesis test, there is enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the click rates of advertisements without animations and the click rates of advertisements with animations is less than 0.
-
Based on the results of the hypothesis test, there is not enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the click rates of advertisements without animations and the click rates of advertisements with animations is less than 0.
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