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Posted about 1 month ago

Jumbo eggs in Australia, on average, are supposed to weigh 68 g68 \mathrm{~g}. Tala is in charge of a quality control test that involves weighing a sample of eggs to test H0:μ=68 gH_{0}: \mu=68 \mathrm{~g} versus Ha:μ68 gH_{\mathrm{a}}: \mu \neq 68 \mathrm{~g}, where μ\mu is the mean weight of the eggs in a batch.

Tala sampled 12 eggs from a batch and found a sample mean weight of 68.5 g68.5 \mathrm{~g} and a standard deviation of 1 g1 \mathrm{~g}. She calculated a test statistic of t1.73t \approx 1.73 and an approximate PP-value of 0.111 . Assume that the conditions for inference were met.

Is there sufficient evidence at the α=0.10\alpha=0.10 level to conclude that the mean weight of the eggs in this batch is not equal to 68 g68 \mathrm{~g} ?

Choose 1 answer:
(A) Yes, because 1.73>0.1111.73>0.111.
(B) No, because 1.73>0.1111.73>0.111.
(c) Yes, because 0.111>0.100.111>0.10.
(D) No, because 0.111>0.100.111>0.10.
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Answer from Sia
Posted about 1 month ago
Solution by Steps
step 1
Identify the null hypothesis H0 H_0 and the alternative hypothesis Ha H_a : H0:μ=68g H_0: \mu = 68 \, \text{g} Ha:μ68g H_a: \mu \neq 68 \, \text{g}
step 2
Given the sample mean xˉ=68.5g\bar{x} = 68.5 \, \text{g}, sample standard deviation s=1gs = 1 \, \text{g}, and sample size n=12n = 12, the test statistic t t is calculated as: t=xˉμs/n1.73 t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \approx 1.73
step 3
The p-value associated with the test statistic t1.73 t \approx 1.73 is approximately 0.111
step 4
Compare the p-value to the significance level α=0.10\alpha = 0.10: p-value=0.111 \text{p-value} = 0.111 α=0.10 \alpha = 0.10 Since 0.111>0.10 0.111 > 0.10 , we fail to reject the null hypothesis H0 H_0
Key Concept
p-value comparison with significance level
If the p-value is greater than the significance level α\alpha, we fail to reject the null hypothesis.

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