Question

1. According to a survey, working men reported doing 63.1 minutes of household chores a day, while working women reported tackling 81 minutes daily. But when examined more closely, millennial men reported doing just as many household chores as the average working women, 81 minutes, compared to an average of 55 minutes among both boomer men and Gen Xers. The information that follows is adapted from these data and is based on random samples of 1146 men and 795 women.

	Mean	Standard Deviation	n
All Women	81	10.4	795
All Men	63.1	16.7	1,146
Millennials	81	9.2	355
Boomers	55	13.9	465
Xers	55	10.5	326

(a)

Construct a 95% confidence interval for the average time all men spend doing household chores. (Round your answers to one decimal place.)

minutes to minutes

(b)

Construct a 95% confidence interval for the average time women spend doing household chores. (Round your answers to one decimal place.)

minutes to minutes

2. A survey is designed to estimate the proportion of sports utility vehicles (SUVs) being driven in the state of California. A random sample of 500 registrations are selected from a Department of Motor Vehicles database, and 26 are classified as SUVs.

(a)

Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

(b)

How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

increase the sample size n increase z_α/2 by decreasing the confidence coefficient conduct a non-random sample increase z_α/2 by increasing the confidence coefficient decrease z_α/2 by increasing the confidence coefficient decrease the sample size n decrease z_α/2 by decreasing the confidence coefficient

3.

A small amount of the trace element selenium, 50–200 micrograms (µg) per day, is considered essential to good health. Suppose that random samples of 40 adults were selected from two regions of the United States and that each person's daily selenium intake was recorded. The means and standard deviations of the selenium daily intakes for the two groups are shown in the table.

	Region
	1	2
Sample Mean (µg)	167.6	140.7
Sample Standard Deviation (µg)	23.7	17.8

Find a 95% confidence interval for the difference

(μ₁ − μ₂)

in the mean selenium intakes for the two regions. (Round your answers to three decimal places.)

µg to µg

Interpret this interval.

We are 95% confident that the difference in the average daily selenium intake for the samples taken from Region 1 and Region 2 is within the interval. The probability that the difference in the average daily selenium intake for the populations in Region 1 and Region 2 is exactly in the middle of the interval is 95%.     We are 95% confident that the difference in the average daily selenium intake for the populations in Region 1 and Region 2 is within the interval. The probability that the difference in the average daily selenium intake for the populations in Region 1 and Region 2 is within the interval is 95%. The daily selenium intake is within the interval for 95% of the populations in Region 1 and Region 2.

4.

Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties? A random sample of 59 plain M&M'S contained 13 red candies, and another random sample of 31 peanut M&M'S contained 9 red candies. (Use p₁ for the proportion of red candies in plain M&M'S and p₂ for the proportion of red candies in peanut M&M'S.)

(a)

Construct a 95% confidence interval for the difference in the proportions of red candies for the plain and peanut varieties

(p₁ − p₂).

(Round your answers to three decimal places.)

to

(b)

Based on the confidence interval in part (a), can you conclude that there is a difference in the proportions of red candies for the plain and peanut varieties? Explain.

Since the value p₁ − p₂ = 0 is not in the confidence interval, it is possible that p₁ = p₂. We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S. Since the value p₁ − p₂ = 0 is in the confidence interval, it is possible that p₁ = p₂. We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S.     Since the value p₁ − p₂ = 0 is in the confidence interval, it is very unlikely that p₁ = p₂. We should conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S. Since the value p₁ − p₂ = 0 is not in the confidence interval, it is very unlikely that p₁ = p₂. We should conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S.

Answer 1

Question 1:

a)

b)   

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