SOLUTION: 8.34 Working Women In an Advertising Age white paper concerning the changing role of women as “breadwinners” in the American family, it was reported that according to their

Question 1194224: 8.34 Working Women In an Advertising Age
white paper concerning the changing role of women as
“breadwinners” in the American family, it was
reported that according to their survey with JWT,
working men reported doing 54 minutes of household
chores a day, while working women reported tackling
72 minutes daily. But when examined more closely,
Millennial men reported doing just as many household
chores as the average working women, 72 minutes,
compared to an average of 54 minutes among both
Boomer men and Xer men.6 The information that follows is adapted from these data and is based on random samples of 1136 men and 795 women.
Standard
Mean Deviation n
All Women 72 10.4 795
All Men 54 12.7 1136
Millennial 72 9.2 345
Boomers 54 13.9 475
Xers 54 10.5 316
a. Construct a 95% confidence interval for the average
time all men spend doing household chores.
b. Construct a 95% confidence interval for the average
time women spend doing household chores
Answer by proyaop(69) (Show Source): You can put this solution on YOUR website!
**a. Construct a 95% Confidence Interval for the Average Time All Men Spend Doing Household Chores**
* **Given:**
* Sample Mean (x̄) = 54 minutes
* Sample Standard Deviation (s) = 12.7 minutes
* Sample Size (n) = 1136 men
* Confidence Level = 95%
* **Find the Critical Value (zα/2):**
* For a 95% confidence level, α = 0.05
* zα/2 = 1.96 (from the standard normal distribution table)
* **Calculate the Standard Error of the Mean (SEM):**
* SEM = s / √n
* SEM = 12.7 / √1136
* SEM ≈ 0.377
* **Calculate the Margin of Error (ME):**
* ME = zα/2 * SEM
* ME = 1.96 * 0.377
* ME ≈ 0.739
* **Construct the Confidence Interval:**
* Lower Limit = x̄ - ME = 54 - 0.739 = 53.261 minutes
* Upper Limit = x̄ + ME = 54 + 0.739 = 54.739 minutes
* **95% Confidence Interval for All Men:** (53.261 minutes, 54.739 minutes)
**b. Construct a 95% Confidence Interval for the Average Time Women Spend Doing Household Chores**
* **Given:**
* Sample Mean (x̄) = 72 minutes
* Sample Standard Deviation (s) = 10.4 minutes
* Sample Size (n) = 795 women
* Confidence Level = 95%
* **Find the Critical Value (zα/2):**
* Same as part (a): zα/2 = 1.96
* **Calculate the Standard Error of the Mean (SEM):**
* SEM = s / √n
* SEM = 10.4 / √795
* SEM ≈ 0.368
* **Calculate the Margin of Error (ME):**
* ME = zα/2 * SEM
* ME = 1.96 * 0.368
* ME ≈ 0.721
* **Construct the Confidence Interval:**
* Lower Limit = x̄ - ME = 72 - 0.721 = 71.279 minutes
* Upper Limit = x̄ + ME = 72 + 0.721 = 72.721 minutes
* **95% Confidence Interval for All Women:** (71.279 minutes, 72.721 minutes)
**Interpretation:**
* We are 95% confident that the true average time all men spend on household chores lies between 53.261 and 54.739 minutes.
* We are 95% confident that the true average time all women spend on household chores lies between 71.279 and 72.721 minutes.

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