The managers of a home improvement chain are trying to decide if the chain should switch the type of paint that it uses for its house brand. The chain developed a proprietary method to test and measure the paint for consistent color tone between batches, which it calls the consistency rating. The company then found the consistency rating for 11 of the same colors from each type of paint. Assume that the conditions for this hypothesis test are satisfied. The company tests the paired data, where α=0.10, in order to evaluate the claim that the true mean difference between the current paint rating and the new paint rating is significantly differe
The managers of a home improvement chain are trying to decide if the chain should switch the type of paint that it uses for its house brand. The chain developed a proprietary method to test and measure the paint for consistent color tone between batches, which it calls the consistency rating. The company then found the consistency rating for 11 of the same colors from each type of paint. Assume that the conditions for this hypothesis test are satisfied.
The company tests the paired data, where α=0.10, in order to evaluate the claim that the true mean difference between the current paint rating and the new paint rating is significantly different from zero.
(a) H0:μd=0, Ha:μd≠0, which is a two-tailed test.
|
Pair |
Current Paint |
New Paint |
|
1 |
64 |
68 |
|
2 |
81 |
89 |
|
3 |
54 |
54 |
|
4 |
71 |
85 |
|
5 |
63 |
66 |
|
6 |
78 |
91 |
|
7 |
58 |
57 |
|
8 |
72 |
75 |
|
9 |
73 |
66 |
|
10 |
85 |
92 |
|
11 |
68 |
65 |
The ratings (given as percentages) for the current paint and the new paint are provided above.
(b) Use a TI-83, TI-83 Plus, or TI-84 calculator to test the paired data and evaluate the claim that the true mean difference is significantly different from zero. Calculate the sample differences using Current−New. Identify the test statistic, t, and p-value from the calculator output.
- Round your test statistic to two decimal places and your p-value to three decimal places.
Provide your answer below:
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
