Q1
Randomly sampled employees at an office were asked to take part in a survey about overtime. The office manager wanted to find out how many employees worked overtime in the last week. The proportion of employees that worked overtime was 0.83, with a margin of error of 0.11.
Construct a confidence interval for the proportion of employees that worked overtime in the last week.
Q2
Amy, a nature photographer, randomly sampled photographs she took within the last year. She wanted to find out how many of her photographs contained flowers. The proportion of photographs that had flowers was 0.61, with a margin of error of 0.04.
Construct a confidence interval for the proportion of her photographs taken within the last year contained flowers.
Q3
A researcher is trying to estimate the population mean for a certain set of data. The sample mean is 45, and the error bound for the mean is 9, at a 99.7% confidence level. (So, x¯=45 and EBM = 9.) Find and interpret the confidence interval estimate.
Ans:
We can estimate, with 99.7% confidence that the true value of the population mean is between 42 and 48.
We can estimate, with 99.7% confidence that the true value of the population mean is between 36 and 54.
We can estimate, with 99.7% confidence that the true value of the population mean is between 45 and 54.
We can estimate, with 99.7% confidence that the true value of the population mean is between −36 and 54.
We can estimate, with 99.7% confidence that the true value of the population mean is between 39 and 51.
We can estimate, with 99.7% confidence that the true value of the population mean is between 36 and 45.
Q4
Randomly sampled math majors at a large university were asked to take part in a survey about the curriculum. The dean wanted to find out how challenging the math coursework was for students. The proportion of math majors that stated the curriculum was challenging was 0.92, with a margin of error of 0.07.
Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging.
Q5
A technician randomly sampled repair logs for computers at a university. He wanted to find out how many times the computers were repaired. The proportion of computers that were repaired more than three times in the last two years was 0.24, with a margin of error of 0.03.
Construct a confidence interval for the proportion of university computers that were repaired more than three times in the last two years.
Q6
A company sells juice in one-quart bottles. In a quality control test, the company found the mean volume of juice in a random sample of bottles was x¯=27 ounces, with a margin of error of 4 ounces.
Construct a confidence interval for the mean number of ounces of juice bottled by this company.
Q7 A marine biologist is interested in whether the Chinook salmon, a particular species of salmon in the Pacific Northwest, are getting smaller within the last decade. In a random sample of this species of salmon, she found the mean length was x¯=36 inches with a margin of error of 9 inches.
Construct a confidence interval for the mean length of Chinook salmon.
Q8
In Boston, a popular restaurant recently added a delivery option. In reviewing the sales for this new delivery service, the restaurant found the mean delivery orders in a random sample of Friday nights was x¯=48 orders, with a margin of error of 12 orders.
Construct a confidence interval for the mean number of delivery orders on a Friday night.
Q9
A production manager randomly sampled production lines at a factory that produces automobiles. She wanted to find out how many production lines caused defects in newly produced automobiles. The proportion of production lines that caused defects was 0.08, with a margin of error of 0.01.
Construct a confidence interval for the proportion of production lines that caused defects.
Q10
A contest for free movie tickets had contestants estimate the number of gumballs in a large bowl. In reviewing the results of a random sample of guesses, a contestant regulator found the mean guess was x¯=136 gumballs, with a margin of error of 13 gumballs.
Construct a confidence interval for the mean number of guesses.
Q11
On a busy Sunday morning, a waitress randomly sampled customers about their preference for morning beverages. Specifically, she wanted to find out how many people preferred coffee over tea. The proportion of customers that preferred coffee was 0.42, with a margin of error of 0.07.
Construct a confidence interval for the proportion of customers that preferred coffee.
Q12
A bowling competition had teams competing for the highest number of strikes during a single bowling game. In reviewing the results of a random sample of teams for this bowling competition, the score keeper found the mean number of strikes was x¯=19, with a margin of error of 3.
Construct a confidence interval for the mean number of strikes.
Q13
A random sample of registered voters were asked about an issue on the ballot of an upcoming election. The proportion of those surveyed who plan to vote “Yes” on the issue is 0.54, with a margin of error of 0.06.
Construct a confidence interval for the proportion of registered voters that plan to vote “Yes” on the issue.
Q14
Randomly sampled employees at an office were asked to take part in a survey about overtime. The office manager wanted to find out how many employees worked overtime in the last week. The proportion of employees that worked overtime was 0.83, with a margin of error of 0.11.
Construct a confidence interval for the proportion of employees that worked overtime in the last week.
Solution
Q1
Randomly sampled employees at an office were asked to take part in a survey about overtime. The office manager wanted to find out how many employees worked overtime in the last week. The proportion of employees that worked overtime was 0.83, with a margin of error of 0.11.
Construct a confidence interval for the proportion of employees that worked overtime in the last week.
Ans: (0.72,0.94)
Q2
Amy, a nature photographer, randomly sampled photographs she took within the last year. She wanted to find out how many of her photographs contained flowers. The proportion of photographs that had flowers was 0.61, with a margin of error of 0.04.
Construct a confidence interval for the proportion of her photographs taken within the last year contained flowers.
Ans: (0.57,0.65)……………..please follow the link below to purchase all the solutions at just $10
