A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are n = 195, x=6.58, s= 1.93. Use a 0.10 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? O A. Ho: H<7.00 H₁: μ>7.00 O C. Ho: μ=7.00 H₁: μ#7.00 OB. Ho: μ=7.00 H₁: H<7.00 O D. Ho: μ=7.00 H₁:μ> 7.00

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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:

 
Reject or Not Reject  H0. There is sufficient or insufficient  evidence to conclude that the mean of the population of ratings is less than, greater than, equal to , or  not equal to   6.00
**Speed Dating Ratings Statistical Analysis**

A data set about speed dating includes "like" ratings of male dates made by female dates. The summary statistics are: 
- Sample size (n) = 195
- Sample mean (\(\bar{x}\)) = 6.58
- Sample standard deviation (s) = 1.93

**Objective**: Test the claim that the population mean of such ratings is less than 7.00 using a 0.10 significance level. Assume a simple random sample has been selected.

**Tasks**:
- Identify the null and alternative hypotheses
- Determine the test statistic
- Calculate the P-value
- State the final conclusion addressing the original claim

**Hypotheses Options**:

- **Option A**:
  - Null hypothesis (\(H_0\)): \(\mu < 7.00\)
  - Alternative hypothesis (\(H_1\)): \(\mu > 7.00\)

- **Option B**:
  - Null hypothesis (\(H_0\)): \(\mu = 7.00\)
  - Alternative hypothesis (\(H_1\)): \(\mu < 7.00\)

- **Option C**:
  - Null hypothesis (\(H_0\)): \(\mu = 7.00\)
  - Alternative hypothesis (\(H_1\)): \(\mu \neq 7.00\)

- **Option D**:
  - Null hypothesis (\(H_0\)): \(\mu = 7.00\)
  - Alternative hypothesis (\(H_1\)): \(\mu > 7.00\)
Transcribed Image Text:**Speed Dating Ratings Statistical Analysis** A data set about speed dating includes "like" ratings of male dates made by female dates. The summary statistics are: - Sample size (n) = 195 - Sample mean (\(\bar{x}\)) = 6.58 - Sample standard deviation (s) = 1.93 **Objective**: Test the claim that the population mean of such ratings is less than 7.00 using a 0.10 significance level. Assume a simple random sample has been selected. **Tasks**: - Identify the null and alternative hypotheses - Determine the test statistic - Calculate the P-value - State the final conclusion addressing the original claim **Hypotheses Options**: - **Option A**: - Null hypothesis (\(H_0\)): \(\mu < 7.00\) - Alternative hypothesis (\(H_1\)): \(\mu > 7.00\) - **Option B**: - Null hypothesis (\(H_0\)): \(\mu = 7.00\) - Alternative hypothesis (\(H_1\)): \(\mu < 7.00\) - **Option C**: - Null hypothesis (\(H_0\)): \(\mu = 7.00\) - Alternative hypothesis (\(H_1\)): \(\mu \neq 7.00\) - **Option D**: - Null hypothesis (\(H_0\)): \(\mu = 7.00\) - Alternative hypothesis (\(H_1\)): \(\mu > 7.00\)
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The given summary statistics is n=195,x¯=6.58,s=1.93.

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