Question

A fast-food company advertises that the pre-cooked weight for its half-pound burgers is, on average, 0.5 lbs. Alvaro is in charge of a quality control test of H₀ : p=0.5 lbs versus H : +0.5 lbs, where u is the mean weight of all burgers in a batch. Alvaro took a random sample of 30 burgers from a batch and found a mean weight of 0.49 lbs and a sample standard deviation of 0.04 lbs. Based on these results, he calculated a test statistic oft -1.37 and a P-value of approximately 0.181. Assuming the conditions for inference were met, what is an appropriate conclusion at the a = significance level?

A. This is strong evidence that the mean weight is different than 0.5 lbs.
B. Reject H₀. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs.
C. Fail to reject H. This is strong evidence that the mean weight is different than 0.5 lbs.
D. Fail to reject H₀. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs

Answer 1

P-value exceeding α and inconclusive t-statistic lead to failure to reject H₀: burgers' mean weight likely remains at 0.5 lbs. Option D) is correct.

Here's the reasoning:

P-value (0.181) is greater than the significance level (a): A P-value greater than the chosen significance level doesn't provide enough evidence to reject the null hypothesis (H₀).

Test statistic (t -1.37) is inconclusive: While the t-statistic is negative, indicating a potential difference from the hypothesized mean (0.5 lbs), its absolute value is not sufficiently extreme to reject the null hypothesis based on the chosen significance level.

Therefore, based on the available information, we cannot conclude that the mean weight of the burgers is different from 0.5 lbs. We need more evidence, such as a lower P-value or a more extreme test statistic, to reject the null hypothesis and claim a significant difference.

The correct answer is D. Fail to reject H₀. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs.