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 $\mathrm{P}$-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 $\mathrm{P}$-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 ⋮ Interpret the p-value: The p-value is a measure of the strength of evidence against the null hypothesis. A small p-value (typically less than α) indicates strong evidence against the null hypothesis, leading to its rejection. ‖ ‖ step 2 ⋮ Compare p-value and α: The p-value obtained from the test (0.181) is compared with the significance level α (0.05). ‖ ‖ step 3 ⋮ Make a decision: Since the p-value is greater than α, there is not enough evidence to reject the null hypothesis. ‖ ***D*** ∻Key Concept∻ ⚹p-value and Decision Making in Hypothesis Testing⚹ ∻Explanation∻ ⚹In hypothesis testing, if the p-value is greater than the significance level α, we fail to reject the null hypothesis. This indicates that there is not enough evidence to support the alternative hypothesis.⚹◊What is the formula for calculating the test statistic in hypothesis testing?⍭ Generate me a similar question◊

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