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. (b) t≈−1.91 , p-value is approximately 0.085 (c) Which of the following are appropriate conclusions for this hypothesis test? Select all that apply. Select all that apply: Fail to reject the null hypothesis that the true mean difference between the current paint rating and the new paint rating is equal to zero. Reject the null hypothesis that the true mean difference between the current paint rating and the new paint rating is equal to zero. There is sufficient evidence at the α=0.10 level of significance to suggest that the true mean difference between the consistency rating for the current paint and the consistency rating for the new paint is not equal to zero. There is not sufficient evidence at the α=0.10 level of significance to suggest that the true mean difference between the consistency rating for the current paint and the consistency rating for the new paint is not equal to zero.
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.
(b) t≈−1.91 , p-value is approximately 0.085
(c) Which of the following are appropriate conclusions for this hypothesis test? Select all that apply.
Select all that apply:
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Fail to reject the null hypothesis that the true mean difference between the current paint rating and the new paint rating is equal to zero.
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Reject the null hypothesis that the true mean difference between the current paint rating and the new paint rating is equal to zero.
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There is sufficient evidence at the α=0.10 level of significance to suggest that the true mean difference between the consistency rating for the current paint and the consistency rating for the new paint is not equal to zero.
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There is not sufficient evidence at the α=0.10 level of significance to suggest that the true mean difference between the consistency rating for the current paint and the consistency rating for the new paint is not equal to zero.
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