One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife's score Husband's score 21 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (c) O Part (d) O Part (e) O Part () O Part (g) O Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (1) Alpha (Enter an exact number as an integer, fraction, or decimal.) a= (ii) Decision: O reject the null hypothesis O do not reject the null hypothesis (ii) Reason for decision: p-value > a, we reject the null hypothesis. O Since p-value > a, we do not reject the null hypothesis. O Since p-value
One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife's score Husband's score 21 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (c) O Part (d) O Part (e) O Part () O Part (g) O Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (1) Alpha (Enter an exact number as an integer, fraction, or decimal.) a= (ii) Decision: O reject the null hypothesis O do not reject the null hypothesis (ii) Reason for decision: p-value > a, we reject the null hypothesis. O Since p-value > a, we do not reject the null hypothesis. O Since p-value
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![**Educational Website Content**
**Understanding Hypothesis Testing in Marital Satisfaction Studies**
In a study examining the marital satisfaction of dual-career couples, participants were asked to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." Ratings spanned from 1 (strongly agree) to 5 (strongly disagree). The table below shows paired responses from husbands and wives, aiming to assess if the mean difference in satisfaction levels (husband vs. wife) is negative. A negative value indicates higher satisfaction for husbands.
**Data Table:**
| Wife’s Score | 3 | 3 | 3 | 3 | 4 | 2 | 1 | 1 | 2 | 4 |
|--------------|---|---|---|---|---|---|---|---|---|---|
| Husband’s Score | 2 | 1 | 2 | 3 | 2 | 1 | 1 | 1 | 2 | 4 |
**Note:** Assume the underlying population is normally distributed when using Student’s t-distribution (verify this assumption if not given).
**Hypothesis Test at 5% Significance Level:**
**Parts of the Problem:**
- **Part (a) to (h):** (Detailed exploration or application items, expand if instructions or data are available)
**Indicate the Correct Decision:**
1. **(i) Alpha (α):** Enter the alpha value (Exact number as integer, fraction, or decimal).
2. **(ii) Decision:**
- [ ] Reject the null hypothesis
- [ ] Do not reject the null hypothesis
3. **(iii) Reason for Decision:**
- [ ] Since p-value > α, we reject the null hypothesis.
- [ ] Since p-value > α, we do not reject the null hypothesis.
- [ ] Since p-value < α, we reject the null hypothesis.
- [ ] Since p-value < α, we do not reject the null hypothesis.
4. **(iv) Conclusion:**
- [ ] There is sufficient evidence to show that, on average, the husbands are more pleased than the wives with the division of childcare.
- [ ] There is not sufficient evidence to show that, on average, the husbands are more pleased than the wives with the division of childcare.
This exercise tests your ability to apply statistical analysis in real-world](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4898dfb-9f02-4356-a947-f4e80c01cbb7%2F2ba9a70d-650e-4690-8db0-4c07045e6605%2Fqukq6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
**Understanding Hypothesis Testing in Marital Satisfaction Studies**
In a study examining the marital satisfaction of dual-career couples, participants were asked to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." Ratings spanned from 1 (strongly agree) to 5 (strongly disagree). The table below shows paired responses from husbands and wives, aiming to assess if the mean difference in satisfaction levels (husband vs. wife) is negative. A negative value indicates higher satisfaction for husbands.
**Data Table:**
| Wife’s Score | 3 | 3 | 3 | 3 | 4 | 2 | 1 | 1 | 2 | 4 |
|--------------|---|---|---|---|---|---|---|---|---|---|
| Husband’s Score | 2 | 1 | 2 | 3 | 2 | 1 | 1 | 1 | 2 | 4 |
**Note:** Assume the underlying population is normally distributed when using Student’s t-distribution (verify this assumption if not given).
**Hypothesis Test at 5% Significance Level:**
**Parts of the Problem:**
- **Part (a) to (h):** (Detailed exploration or application items, expand if instructions or data are available)
**Indicate the Correct Decision:**
1. **(i) Alpha (α):** Enter the alpha value (Exact number as integer, fraction, or decimal).
2. **(ii) Decision:**
- [ ] Reject the null hypothesis
- [ ] Do not reject the null hypothesis
3. **(iii) Reason for Decision:**
- [ ] Since p-value > α, we reject the null hypothesis.
- [ ] Since p-value > α, we do not reject the null hypothesis.
- [ ] Since p-value < α, we reject the null hypothesis.
- [ ] Since p-value < α, we do not reject the null hypothesis.
4. **(iv) Conclusion:**
- [ ] There is sufficient evidence to show that, on average, the husbands are more pleased than the wives with the division of childcare.
- [ ] There is not sufficient evidence to show that, on average, the husbands are more pleased than the wives with the division of childcare.
This exercise tests your ability to apply statistical analysis in real-world
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