A fast-food company advertises that the pre-cooked weight for its halfpound burgers is, on average, $0.5 \mathrm{lbs}$. Alvaro is in charge of a quality control test of $H_{0}: \mu=0.5 \mathrm{lbs}$ 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 $0.49 \mathrm{lbs}$ and a sample standard deviation of $0.04 \mathrm{lbs}$. 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 $0.5 \mathrm{lbs}$.
(B) Reject $H_{0}$. This isn't enough evidence to conclude that the mean weight is different than $0.5 \mathrm{lbs}$.
(c) Fail to reject $H_{0}$. This is strong evidence that the mean weight is different than $0.5 \mathrm{lbs}$.
(D) Fail to reject $H_{0}$. This isn't enough evidence to conclude that the mean weight is different than $0.5 \mathrm{lbs}$.

Question

A fast-food company advertises that the pre-cooked weight for its halfpound burgers is, on average, $0.5 \mathrm{lbs}$. Alvaro is in charge of a quality control test of $H_{0}: \mu=0.5 \mathrm{lbs}$ 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 $0.49 \mathrm{lbs}$ and a sample standard deviation of $0.04 \mathrm{lbs}$. 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 $0.5 \mathrm{lbs}$.
(B) Reject $H_{0}$. This isn't enough evidence to conclude that the mean weight is different than $0.5 \mathrm{lbs}$.
(c) Fail to reject $H_{0}$. This is strong evidence that the mean weight is different than $0.5 \mathrm{lbs}$.
(D) Fail to reject $H_{0}$. This isn't enough evidence to conclude that the mean weight is different than $0.5 \mathrm{lbs}$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Compare the p-value to the significance level α to determine whether to reject the null hypothesis. ‖ ‖ step 2 ⋮ The p-value is 0.181, which is greater than the significance level of 0.05. ‖ ‖ step 3 ⋮ Since the p-value is greater than α, we fail to reject the null hypothesis. ‖ ‖ step 4 ⋮ There is not enough evidence to conclude that the mean weight is different from 0.5 lbs. ‖ ***D*** ∻Key Concept∻ ⚹p-value and significance level comparison⚹ ∻Explanation∻ ⚹If the p-value is greater than the significance level, we fail to reject the null hypothesis, indicating insufficient evidence against it.⚹◊What is the critical value for a two-tailed test at a 0.05 significance level?⍭ Generate me a similar question◊

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