Respuesta :
(a) True life expectancy is shorter than advertised.
(b) True life expectancy is not less than advertised.
Significance Level:
The significance level, also called alpha or α, is a measure of the strength of evidence that must be present in the sample before the null hypothesis can be rejected and an effect can be concluded to be statistically significant. The researcher determines the significance level before conducting the experiment.
The significance level is the probability of rejecting the null hypothesis if it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that there is a difference when there really isn't. A low significance level indicates that you need stronger evidence before rejecting the null hypothesis.
According to the question:
The hypothesis for this test can be defined as follows:
H₀: True life expectancy is not less than stated value. H. µ > 750 hours.
Hₐ: Actual life expectancy is less than stated. H. μ < 750 hours.
The test is left-tailed.
Decision Rule:
If the p-value of the test is less than the significance level (α), then the null hypothesis is rejected and vice versa.
The p-value for the test is calculated as p-value = 0.016
(a) The significance level is α = 0.05.
p-value = 0.016 < α = 0.05.
The p-value for the test is less than the significance level, so the null hypothesis is rejected.
Therefore, the conclusion of the test at the 5% significance level is that true life expectancy is shorter than advertised.
(b) The significance level is α = 0.01.
p-value = 0.016 > α = 0.01.
The p-value for the test is above the significance level, so the null hypothesis could not be rejected.
Therefore, at the 5% significance level, the conclusion of the test is that the true life expectancy is not shorter than the advertised life expectancy.
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