## (CORRECT ANSWER) MATH225N Week 6 Assignment : Point Estimates, Margins of Error and Confidence Intervals

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**Question**

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.

Provide your answer below:

Ans:

**Question**

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.

Select the correct answer below:

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.

Ans.

** ****Question**

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.

Provide your answer below:

Ans:

**Question **

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.

**Question**

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.

Ans.

**Question**

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.

Ans.

**Question**

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¯=31 ounces, with a margin of error of 3 ounces.

Construct a confidence interval for the mean number of ounces of juice bottled by this company.

Confidence interval is

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