Regular Bata on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet H2 26 26 0.79911 Ib 0.00445 Ib 0.81326 Ib 0.00759 Ib a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? O A. Ho: H1 =H2 B. Ho: H1 = H2 H: > H2 H: P1

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**Hypothesis Testing on Soda Can Weights**

Data on the weights (in pounds) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized below. Assume that the two samples are independent, simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts.

**Summary Table:**

|           | Diet    | Regular  |
|-----------|---------|----------|
| μ         | μ₁      | μ₂       |
| n         | 26      | 26       |
| x̄        | 0.79911 lb | 0.81326 lb |
| s         | 0.00445 lb | 0.00759 lb |

**a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.**

**What are the null and alternative hypotheses?**

- **A.** 
  - \( H_0: \mu_1 = \mu_2 \)
  - \( H_1: \mu_1 > \mu_2 \)

- **B.** 
  - \( H_0: \mu_1 = \mu_2 \) ✔
  - \( H_1: \mu_1 < \mu_2 \)

- **C.** 
  - \( H_0: \mu_1 \neq \mu_2 \)
  - \( H_1: \mu_1 < \mu_2 \)

- **D.** 
  - \( H_0: \mu_1 = \mu_2 \)
  - \( H_1: \mu_1 \neq \mu_2 \)

The test statistic, t, is [ ]

(Round to two decimal places as needed.)
Transcribed Image Text:**Hypothesis Testing on Soda Can Weights** Data on the weights (in pounds) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized below. Assume that the two samples are independent, simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. **Summary Table:** | | Diet | Regular | |-----------|---------|----------| | μ | μ₁ | μ₂ | | n | 26 | 26 | | x̄ | 0.79911 lb | 0.81326 lb | | s | 0.00445 lb | 0.00759 lb | **a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.** **What are the null and alternative hypotheses?** - **A.** - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 > \mu_2 \) - **B.** - \( H_0: \mu_1 = \mu_2 \) ✔ - \( H_1: \mu_1 < \mu_2 \) - **C.** - \( H_0: \mu_1 \neq \mu_2 \) - \( H_1: \mu_1 < \mu_2 \) - **D.** - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 \neq \mu_2 \) The test statistic, t, is [ ] (Round to two decimal places as needed.)
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