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Listed in the accompanying table are weights (lb) of samples of the contents of cans of regular Coke and Diet Coke. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) to ©. Click the icon to view the data table of can weights.
a. Use a 0.01 significance level to test the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.

What are the null and alternative hypotheses? Assume that population 1 consists of regular Coke and population 2 consists of Diet Coke.
A. B.
C.

D.

The test statistic is (Round to two decimal places as needed.)

Ask by Valdez Cross. in the United States

Mar 27,2025

Question

Part 2 of 6
Points: 0 of 1
Save

Listed in the accompanying table are weights (lb) of samples of the contents of cans of regular Coke and Diet Coke. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) to ©. Click the icon to view the data table of can weights.
a. Use a 0.01 significance level to test the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.

What are the null and alternative hypotheses? Assume that population 1 consists of regular Coke and population 2 consists of Diet Coke.
A. B.
C.

D.

The test statistic is (Round to two decimal places as needed.)

Ask by Valdez Cross. in the United States

Mar 27,2025

UpStudy AI · Accepted Answer

**Step 1. Write the Hypotheses**

Since the claim is that the mean weight of cans of regular Coke (population 1) is greater than the mean weight for Diet Coke (population 2), we set up the hypotheses as follows:

$$
\begin{aligned}
& H_{0}: \mu_1 \le \mu_2 \quad \text{(null hypothesis)}\[1mm]
& H_{1}: \mu_1 > \mu_2 \quad \text{(alternative hypothesis)}
\end{aligned}
$$

This corresponds to choice **B**.

**Step 2. Write the Test Statistic**

Since we do not assume that the population standard deviations are equal and the samples are independent and normally distributed, we use the unpooled (unequal variances) two-sample $$ t $$-test. The test statistic is given by:

$$
t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
$$

where:
- $$\bar{x}_1$$ and $$\bar{x}_2$$ are the sample means for regular Coke and Diet Coke, respectively,
- $$s_1$$ and $$s_2$$ are the sample standard deviations,
- $$n_1$$ and $$n_2$$ are the sample sizes.

After computing this value from the data, be sure to round the test statistic to two decimal places.

Thus, the final answers are:

- **Hypotheses:**  
  $$
  H_0: \mu_1 \le \mu_2 \quad \text{and} \quad H_1: \mu_1 > \mu_2
  $$
- **Test Statistic:**
  $$
  t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
  $$
**Hypotheses:** - $$ H_{0}: \mu_{1} \leq \mu_{2} $$ - $$ H_{1}: \mu_{1} > \mu_{2} $$ **Test Statistic:** $$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $$ (Rounded to two decimal places)

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