The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.56 days. Is this average different for blind dates? A researcher interviewed 51 couples who had recently been on blind dates and found that they averaged 3 days to communicate with each other after the date was over. Their standard deviation was 1.186 days. What can be concluded at the a = 0.01 level of significance? %3D

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### Statistical Hypothesis Testing Example

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.56 days. Is this average different for blind dates? A researcher interviewed 51 couples who had recently been on blind dates and found that they averaged 3 days to communicate with each other after the date was over. Their standard deviation was 1.186 days. What can be concluded at the \(\alpha = 0.01\) level of significance?

#### Steps to Test the Hypothesis

1. **For this study, we should use**  
   (Select an answer)

2. **The null and alternative hypotheses would be:**
    - \(H_0 :\)  
      (Select an answer)  
      \(=?\)
    - \(H_1 :\)  
      (Select an answer)  
      \(=?\)

3. **The test statistic \(t\) =**  
   (Please show your answer to 3 decimal places.)
   \[t = ?\]

4. **The p-value =**  
   (Please show your answer to 4 decimal places.)  
   \[p = ?\]

5. **The p-value is**  
   (Select an answer)  
   \(\alpha\)

6. **Based on this, we should**  
   (Select an answer)  
   (Reject or Fail to Reject) the null hypothesis.

7. **Thus, the final conclusion is that …**  
   - The data suggest the population mean is **significantly different from 3.56** at \(\alpha = 0.01\), so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is different from 3.56.
   - The data suggest the population mean is **not significantly different from 3.56** at \(\alpha = 0.01\), so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is equal to 3.56.
   - The data suggest that the population mean is **not significantly different from 3.56** at \(\alpha = 0.01\), so there is statistically insignificant evidence to conclude that the population mean time
Transcribed Image Text:### Statistical Hypothesis Testing Example The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.56 days. Is this average different for blind dates? A researcher interviewed 51 couples who had recently been on blind dates and found that they averaged 3 days to communicate with each other after the date was over. Their standard deviation was 1.186 days. What can be concluded at the \(\alpha = 0.01\) level of significance? #### Steps to Test the Hypothesis 1. **For this study, we should use** (Select an answer) 2. **The null and alternative hypotheses would be:** - \(H_0 :\) (Select an answer) \(=?\) - \(H_1 :\) (Select an answer) \(=?\) 3. **The test statistic \(t\) =** (Please show your answer to 3 decimal places.) \[t = ?\] 4. **The p-value =** (Please show your answer to 4 decimal places.) \[p = ?\] 5. **The p-value is** (Select an answer) \(\alpha\) 6. **Based on this, we should** (Select an answer) (Reject or Fail to Reject) the null hypothesis. 7. **Thus, the final conclusion is that …** - The data suggest the population mean is **significantly different from 3.56** at \(\alpha = 0.01\), so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is different from 3.56. - The data suggest the population mean is **not significantly different from 3.56** at \(\alpha = 0.01\), so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is equal to 3.56. - The data suggest that the population mean is **not significantly different from 3.56** at \(\alpha = 0.01\), so there is statistically insignificant evidence to conclude that the population mean time
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