Question

Statistics

Posted 5 months ago

```
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 $0.111>0.10$.
```

Sign in to unlock the answer

Answer from Sia

Posted 5 months 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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Unlock Smarter Learning with AskSia Super!

Join Super, our all-in-one AI solution that can greatly improve your learning efficiency.

30% higher accuracy than GPT-4o

Entire learning journey support

The most student-friendly features

Study Other Question