Question 1

A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the margin of error will be 2 months or less?

Accepted Answer

The answer of A researcher is interested in determining the...

Question 2

If the standard deviation of the lifetimes of vacuum cleaners is estimated to be 300 hours, how large of a sample must be taken in order to be 97% confident that the margin of error will not exceed 40 hours?

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The answer of If the standard deviation of the lifetimes...

Question 3

A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that they mine. Assuming that the company reports that the standard deviation of daily output is 200 tons, how many days should they sample so that the margin of error will be 39.2 tons or less?

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Question 4

In a random sample of 400 registered voters, 120 indicated they plan to vote for Candidate A. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Candidate A.

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The answer of In a random sample of 400 registered...

Question 5

A real estate agent wants to estimate the mean selling price of two-bedroom homes in a particular area. She wants to estimate the mean selling price to within $10,000 with an 89.9% level of confidence. The standard deviation of selling prices is unknown but the agent estimates that the highest selling price is $1,000,000 and the lowest is $50,000. How many homes should be sampled?

Accepted Answer

The answer of A real estate agent wants to estimate...

Question 6

The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is taken. The average age in the sample was 22.5 years with a standard deviation of 5 years. Assume the population of consumer ages is normally distributed.
a.Construct a 95% confidence interval for the average age of all the consumers.
b.Construct an 80% confidence interval for the average age of all the consumers.
c.Discuss why the 95% and 80% confidence intervals are different.

Accepted Answer

The answer of The makers of a soft drink want...

Question 7

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers revealed an average age of 28 years with a standard deviation of 10 years. Determine a 95% confidence interval estimate for the average age of all his customers. Assume the population of customer ages is normally distributed.

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The answer of The proprietor of a boutique in New...

Question 8

You are given the following information obtained from a random sample of 4 observations taken from a large, normally distributed population.  Construct a 95% confidence interval for the mean of the population.

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Question 9

If the standard deviation for the lifetimes of washing machines is estimated to be 800 hours, how large a sample must be taken in order to be 97% confident that the margin of error will not exceed 50 hours?

Accepted Answer

The answer of If the standard deviation for the lifetimes...

Question 10

A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of 5 examinations is selected at random and scored. The scores are shown below.  Use Excel to determine an interval estimate for the mean of the population at a 98% confidence level. Interpret your results.

Accepted Answer

The answer of A local university administers a comprehensive examination...

Question 11

A sample of 16 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population. Assume the population of student ages is normally distributed.

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The answer of A sample of 16 students from a...

Question 12

You are given the following information obtained from a random sample of 4 observations from a large, normally distributed population.  
a.What is the point estimate of $\mu$?
b.Construct a 95% confidence interval for $\mu$.
c.Construct a 90% confidence interval for $\mu$.
d.Discuss why the 90% and 95% confidence intervals are different.

Accepted Answer

The answer of You are given the following information obtained...

Question 13

Below you are given ages that were obtained by taking a random sample of 9 undergraduate students.  Use Excel to determine an interval estimate for the mean of the population at a 99% confidence level. Interpret your results.

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The answer of Below you are given ages that were...

Question 14

Fifty students are enrolled in an Economics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90.
a.Calculate the estimate of the standard error of the mean.
b.What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why.
c.Assume the assumption of Part b is met. Provide a 90% confidence interval for the mean grade of all the students in the class.
d.If there were 200 students in the class, what would be the 90% confidence interval for the mean grade of all the students in the class?

Accepted Answer

The answer of Fifty students are enrolled in an Economics...

Question 15

It is known that the variance of a population equals 484. A random sample of 81 observations is going to be taken from the population.
a.With a .80 probability, what statement can be made about the size of the margin of error?
b.With a .80 probability, how large of a sample would have to be taken to provide a margin of error of 3 or less?

Accepted Answer

The answer of It is known that the variance of...

Question 16

For inventory purposes, a grocery store manager wants to estimate the mean number of pounds of cat food sold per month. The estimate is desired to be within 10 pounds with a 95% level of confidence. A pilot study provided a standard deviation of 27.6 pounds. How many months should be sampled?

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The answer of For inventory purposes, a grocery store manager...

Question 17

A random sample of 25 observations was taken from a normally distributed population. The average in the sample was 84.6 with a variance of 400.
a.Construct a 90% confidence interval for $\mu$.
b.Construct a 99% confidence interval for $\mu$.
c.Discuss why the 90% and 99% confidence intervals are different.
d.What would you expect to happen to the confidence interval in part a if the sample size was increased? Be sure to explain your answer.

Accepted Answer

The answer of A random sample of 25 observations was...

Question 18

A statistician selected a sample of 16 accounts receivable and determined the mean of the sample to be $5,000 with a standard deviation of $400. She reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. She did not report what confidence coefficient she had used. Based on the above information, determine the confidence coefficient that was used.

Accepted Answer

The answer of A statistician selected a sample of 16...

Question 19

The monthly starting salaries of students who receive an MBA degree have a standard deviation of $110. What size sample should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less?

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The answer of The monthly starting salaries of students who...

Question 20

The monthly incomes from a random sample of faculty at a university are shown below.  Compute a 90% confidence interval for the mean of the population. The population of all faculty incomes is known to be normally distributed. Give your answer in dollars.

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The answer of The monthly incomes from a random sample...

Quiz 8: Interval Estimation