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 $$ H_{0}: \mu=0.5 $$ lbs versus $$ H_{\mathrm{a}}: \mu
eq 0.5 \mathrm{lbs} $$, where $$ \mu $$ 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 of $$ t \approx-1.37 $$ and a P-value of approximately 0.181 . Assuming the conditions for inference were met, what is an appropriate conclusion at the $$ \alpha=0.05 $$ significance level? Choose 1 answer: (A) Reject $$ H_{0} $$. This is strong evidence that the mean weight is different than 0.5 lbs. (B) Reject $$ H_{0} $$. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs. (C) Fail to reject $$ H_{0} $$. This is strong evidence that the mean weight is different than 0.5 lbs. (D) Fail to reject $$ H_{0} $$. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs.

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 $$ H_{0}: \mu=0.5 $$ lbs versus $$ H_{\mathrm{a}}: \mu 
eq 0.5 \mathrm{lbs} $$, where $$ \mu $$ 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 of $$ t \approx-1.37 $$ and a P-value of approximately 0.181 . Assuming the conditions for inference were met, what is an appropriate conclusion at the $$ \alpha=0.05 $$ significance level? Choose 1 answer: (A) Reject $$ H_{0} $$. This is strong evidence that the mean weight is different than 0.5 lbs. (B) Reject $$ H_{0} $$. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs. (C) Fail to reject $$ H_{0} $$. This is strong evidence that the mean weight is different than 0.5 lbs. (D) Fail to reject $$ H_{0} $$. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs.

UpStudy AI · Accepted Answer

Since the P-value (approximately 0.181) is greater than the significance level (α = 0.05), you do not have enough evidence to reject the null hypothesis. Therefore, the appropriate conclusion is:

(D) Fail to reject H₀. This isn't enough evidence to conclude that the mean weight is different than 0.5 lbs.
Fail to reject $$ H_{0} $$. There isn't enough evidence to conclude that the mean weight is different than 0.5 lbs.

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