Question

Statistics

Posted about 1 month ago

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Jumbo eggs in Australia, on average, are supposed to weigh $68 \mathrm{~g}$. Tala is in charge of a quality control test that involves weighing a sample of eggs to test $H_{0}: \mu=68 \mathrm{~g}$ versus $H_{\mathrm{a}}: \mu \neq 68 \mathrm{~g}$, where $\mu$ is the mean weight of the eggs in a batch.
Tala sampled 12 eggs from a batch and found a sample mean weight of $68.5 \mathrm{~g}$ and a standard deviation of $1 \mathrm{~g}$. She calculated a test statistic of $t \approx 1.73$ and an approximate $P$-value of 0.111 . Assume that the conditions for inference were met.
Is there sufficient evidence at the $\alpha=0.10$ level to conclude that the mean weight of the eggs in this batch is not equal to $68 \mathrm{~g}$ ?
Choose 1 answer:
(A) Yes, because $1.73>0.111$.
(B) No, because $1.73>0.111$.
(c) Yes, because $0.111>0.10$.
(D) No, because $0.111>0.10$.
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Answer from Sia

Posted about 1 month ago

Solution by Steps

step 1

Identify the null hypothesis $H_0$ and the alternative hypothesis $H_a$:
$H_0: \mu = 68 \, \text{g}$
$H_a: \mu \neq 68 \, \text{g}$

step 2

Given the sample mean $\bar{x} = 68.5 \, \text{g}$, sample standard deviation $s = 1 \, \text{g}$, and sample size $n = 12$, the test statistic $t$ is calculated as:
$t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \approx 1.73$

step 3

The p-value associated with the test statistic $t \approx 1.73$ is approximately 0.111

step 4

Compare the p-value to the significance level $\alpha = 0.10$:
$\text{p-value} = 0.111$
$\alpha = 0.10$
Since $0.111 > 0.10$, we fail to reject the null hypothesis $H_0$

Answer

D

Key Concept

p-value comparison with significance level

Explanation

If the p-value is greater than the significance level $\alpha$, we fail to reject the null hypothesis.

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