A cooler bag producing company claims that their coolers keep products cold for 12 hours. A test of hypotheses H₀: µ = 12 versus Ha: µ

Question

A cooler bag producing company claims that their coolers keep products cold for 12 hours. A test of hypotheses H₀: µ = 12 versus Ha: µ < 12 is based on a sample of size n = 33. Suppose that σ is known to be 0.6 and a significance level of 0.05 will be used. Determine the power of the test and interpret the result when µ = 11.75. A) The power of the test is 0.23, which means that 23% of the samples will result in a conclusion to reject H₀: µ = 12 when the true µ is 11.75. B) The power of the test is 0.01, which means that 1% of the samples will result in a conclusion to reject H₀: µ = 12 when the true µ is 11.75. C) The power of the test is 0.77, which means that 77% of the samples will result in a conclusion to reject H₀: µ = 12 when the true µ is 11.75. D) The power of the test is 0.99, which means that 99% of the samples will result in a conclusion to reject H₀: µ = 12 when the true µ is 11.75. E) The power of the test is 0.67, which means that 67% of the samples will result in a conclusion to reject H₀: µ = 12 when the true µ is 11.75.

Quizplus · Accepted Answer

The power of the test can be calculated using the formula: Power = P(Z < (Zα-μ/σ/√n) - Z(μ/σ/√n-Δ)) where Zα-μ/σ/√n is the critical value for the given significance level (0.05) and Z(μ/σ/√n-Δ) is the standard normal value for the alternative hypothesis mean (11.75) and the null hypothesis mean (12) when σ is known to be 0.6. Substituting the given values, we get: Power = P(Z < -1.64 - (-0.42)) = P(Z < -1.22) = 0.77 Therefore, the power of the test is 0.77, which means that 77% of the samples will result in a conclusion to reject H₀: µ = 12 when the true µ is 11.75.

A Cooler Bag Producing Company Claims That Their Coolers Keep