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Math
Posted 3 months ago

A fast-food company advertises that the pre-cooked weight for its halfpound burgers is, on average, 0.5lbs0.5 \mathrm{lbs}. Alvaro is in charge of a quality control test of H0:μ=0.5lbsH_{0}: \mu=0.5 \mathrm{lbs} versus Ha:μ0.5lbsH_{\mathrm{a}}: \mu \neq 0.5 \mathrm{lbs}, where μ\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 0.49lbs0.49 \mathrm{lbs} and a sample standard deviation of 0.04lbs0.04 \mathrm{lbs}. Based on these results, he calculated a test statistic of t1.37t \approx-1.37 and a P\mathrm{P}-value of approximately 0.181.

Assuming the conditions for inference were met, what is an appropriate conclusion at the α=0.05\alpha=0.05 significance level?

Choose 1 answer:
(A) Reject H0H_{0}. This is strong evidence that the mean weight is different than 0.5lbs0.5 \mathrm{lbs}.
(B) Reject H0H_{0}. This isn't enough evidence to conclude that the mean weight is different than 0.5lbs0.5 \mathrm{lbs}.
(C) Fail to reject H0H_{0}. This is strong evidence that the mean weight is different than 0.5lbs0.5 \mathrm{lbs}.
(D) Fail to reject H0H_{0}. This isn't enough evidence to conclude that the mean weight is different than 0.5lbs0.5 \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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