Question

Math

Posted 3 months ago

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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 $H_{\mathrm{a}}: \mu \neq 0.5 \mathrm{lbs}$, 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 $0.5 \mathrm{lbs}$.
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Answer from Sia

Posted 3 months ago

Solution by Steps

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.

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