A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are n= 196, x = 6.87, s = 2.03. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 7.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

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A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are n = 196, x̄ = 6.87, s = 2.03. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 7.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

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

- **A.** \( H_0: \mu = 7.00 \)  
  \( H_1: \mu > 7.00 \)

- **B.** \( H_0: \mu = 7.00 \)  
  \( H_1: \mu \neq 7.00 \)

- **C.** \( H_0: \mu < 7.00 \)  
  \( H_1: \mu > 7.00 \)

- **D.** \( H_0: \mu = 7.00 \)  
  \( H_1: \mu < 7.00 \)

**Determine the test statistic.**  
(Round to two decimal places as needed.)

**Determine the P-value.**  
(Round to three decimal places as needed.)

**State the final conclusion that addresses the original claim.**

\[ \Box \] \( H_0: \text{There is} \) \[ \Box \] \text{evidence to conclude that the mean of the population of ratings is} \[ \Box \] \( 7.00. \)

Click to select your answer(s).
Transcribed Image Text:A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are n = 196, x̄ = 6.87, s = 2.03. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 7.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. **What are the null and alternative hypotheses?** - **A.** \( H_0: \mu = 7.00 \) \( H_1: \mu > 7.00 \) - **B.** \( H_0: \mu = 7.00 \) \( H_1: \mu \neq 7.00 \) - **C.** \( H_0: \mu < 7.00 \) \( H_1: \mu > 7.00 \) - **D.** \( H_0: \mu = 7.00 \) \( H_1: \mu < 7.00 \) **Determine the test statistic.** (Round to two decimal places as needed.) **Determine the P-value.** (Round to three decimal places as needed.) **State the final conclusion that addresses the original claim.** \[ \Box \] \( H_0: \text{There is} \) \[ \Box \] \text{evidence to conclude that the mean of the population of ratings is} \[ \Box \] \( 7.00. \) Click to select your answer(s).
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