A hypothesis test is conducted with respect to the mean weight (in ounces) of potato chip bags form a certain manufacturer. The hypotheses are: H0: = 0.8 and Ha: ≠ 0.8. Which confidence level would support the conclusion that there is insufficient evidence to reject H0 when = 0.03?
a) 97% b) 94% c) 95% d) 98.5% e) 90%
To determine the confidence level that would support the conclusion of insufficient evidence to reject the null hypothesis (H0), we need to compare the significance level (alpha, α) with the p-value obtained from the hypothesis test.
In this case, the significance level (α) is given as 0.03 or 3%. If the p-value is greater than 0.03, we would fail to reject the null hypothesis (insufficient evidence). If the p-value is less than or equal to 0.03, we would reject the null hypothesis (sufficient evidence).
The confidence level is equal to 1 minus the significance level, so the confidence level that supports the conclusion of insufficient evidence for α = 0.03 would be:
Confidence level = 1 - α
Confidence level = 1 - 0.03
Confidence level = 0.97 or 97%
Therefore, the correct answer is (a) 97%
To determine which confidence level would support the conclusion of insufficient evidence to reject H0 at α = 0.03, we need to compare the α value (significance level) to the confidence level.
In this case, α = 0.03 means the test has a 3% chance of making a Type I error (rejecting H0 when it is actually true).
So we need to find a confidence level that leaves a probability of 3% or less in the tails of the distribution (since it matches with the α value).
Looking at the answer choices:
a) 97% confidence level means a significance level of 1% (100% - 97% = 3%). This is not equal to α = 0.03, so it's not the answer.
b) 94% confidence level means a significance level of 6% (100% - 94% = 6%). This is not equal to α = 0.03, so it's not the answer.
c) 95% confidence level means a significance level of 5% (100% - 95% = 5%). This is equal to α = 0.03, so it could be the answer.
d) 98.5% confidence level means a significance level of 1.5% (100% - 98.5% = 1.5%). This is not equal to α = 0.03, so it's not the answer.
e) 90% confidence level means a significance level of 10% (100% - 90% = 10%). This is not equal to α = 0.03, so it's not the answer.
Therefore, the confidence level that would support the conclusion of insufficient evidence to reject H0 when α = 0.03 is c) 95%.