Question 1

You are given the following information obtained from a random sample of 5 observations taken from a large population.  ​
Construct a 95% confidence interval for the mean of the population, assuming the population has a normal distribution.

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Question 2

The monthly incomes from a random sample of workers in a factory are shown below.  ​ 
a.
Compute the standard error of the mean (in dollars).
b.
Compute the margin of error (in dollars) at 95% confidence.
c.
Compute a 95% confidence interval for the mean of the population.Assume the population has a normal distribution.Give your answer in dollars.
​

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Question 3

A random sample of 95 students at a local university showed that they work an average of 48 hours per month with a standard deviation of 12 hours.Compute a 95% confidence interval for the mean of the population.

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Question 4

A random sample of 100 credit sales in a department store showed an average sale of $120.00.From past data, it is known that the standard deviation of the population is $40.00.
a.
Determine the standard error of the mean.
b.
With a .95 probability, determine the margin of error.
c.
What is the 95% confidence interval of the population mean?

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Question 5

It is known that the variance of a population equals 576.A random sample of 144 observations is going to be taken from the population.
a.
With a .95 probability, what statement can be made about the size of the margin of error?
b.
With a .95 probability, how large of a sample would have to be taken to provide a margin of error of 6 or less?

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Question 6

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 16 pieces of carry-on luggage was weighed.The average weight was 20 pounds.Assume that we know the standard deviation of the population to be 8 pounds.Also, assume the population is normally distributed.
a.
Determine a 97% confidence interval estimate for the population mean weight of the carry-on luggage.
b.
Determine a 95% confidence interval estimate for the population mean weight of the carry-on luggage.

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Question 7

A random sample of 121 checking accounts at a bank showed an average daily balance of $280.The standard deviation of the population is known to be $66.
a.
Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances? Explain.
b.
Find the standard error of the mean.
c.
Give a point estimate of the population mean.
d.
Construct an 80% confidence interval for the population mean.
e.
Construct a 95% confidence interval for the population mean.

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Question 8

Below you are given ages that were obtained by taking a random sample of 6 undergraduate instructors at a university.Assume the population has a normal distribution.  ​ 
a.
What is the point estimate of μ?
b.
Determine the standard deviation.
c.
Construct a 90% confidence interval for the average age of undergraduate instructors.
d.
Construct a 99% confidence interval for the average age of undergraduate instructors.
e.
Discuss why the 90% and 99% confidence intervals are different.

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Question 9

A sample of 100 students from a large university was taken.The average age in the sample was 22 years with a standard deviation of 4 years.Construct a 95% confidence interval for the average age of the population.

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Question 10

A university planner is interested in determining the percentage of spring semester students who will attend summer school.She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school.
a.
Construct a 95% confidence interval estimate for the percentage of spring semester students who will return to summer school.
b.
Using the results of the pilot study with a .95 probability, how large of a sample would have to be taken to provide a margin of error of 3% or less?

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Question 11

A random sample of 144 checking accounts at a bank showed an average daily balance of $500 and a standard deviation of $60.Develop a 95% confidence interval estimate for the mean of the population.

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Question 12

A new brand of chocolate bar is being market tested.Four hundred of the new chocolate bars were given to consumers to try.The consumers were asked whether they liked or disliked the chocolate bar.You are given their responses below.  ​ 
a.
What is the point estimate for the proportion of people who liked the chocolate bar?
b.
Construct a 95% confidence interval for the true proportion of people who liked the chocolate bar.
c.
With a .95 probability, how large of a sample needs to be taken to provide a margin of error of 1.5% or less?
​

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Question 13

A random sample of 49 lunch customers was taken at a restaurant.The average amount of time these customers stayed in the restaurant was 45 minutes with a standard deviation of 14 minutes.
a.
Compute the standard error of the mean.
b.
With a .95 probability, what statement can be made about the size of the margin of error?
c.
Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant.
d.
With a .95 probability, how large of a sample would have to be taken to provide a margin of error of 2.5 minutes or less?

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Question 14

In order to estimate the average electric usage per month, a sample of 256 houses was selected and their electric usage was determined.Assume a population standard deviation of 500 kilowatt-hours.
a.
Determine the standard error of the mean.
b.
With a .95 probability, determine the margin of error.
c.
If the sample mean is 2500 kWh, what is the 95% confidence interval estimate of the population mean?

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Question 15

You are given the following information obtained from a random sample of 6 observations.Assume the population has a normal distribution.  ​ 
a.
What is the point estimate of μ?
b.
Construct an 80% confidence interval for μ.
c.
Construct a 98% confidence interval for μ.
d.
Discuss why the 80% and 98% confidence intervals are different.

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Question 16

If the population standard deviation of the lifetime of washing machines is estimated to be 1000 hours, how large a sample must be taken in order to be 95% confident that the margin of error will not exceed 100 hours?

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Question 17

The makers of a soft drink want to identify the average age of its consumers.A sample of 55 consumers was taken.The average age in the sample was 21 years with a standard deviation of 4 years.
a.
Construct a 95% confidence interval for the true average age of the consumers.
b.
Construct an 80% confidence interval for the true average age of the consumers.
c.
Discuss why the 95% and 80% confidence intervals are different.

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Question 18

The manager of a department store wants to determine the proportion of people who use the store's credit cards for their purchases.What sample size should he take so that, at 95% confidence, the error will not be more than 6%?

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Question 19

In a sample of 200 individuals, 130 indicated they are Democrats.Develop a 95% confidence interval for the proportion of Democrats in the population.

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Question 20

A random sample of 53 observations was taken.The average in the sample was 90 with a variance of 400.
a.
Construct a 98% confidence interval for μ.
b.
Construct a 99% confidence interval for μ.
c.
Discuss why the 98% 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.

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Quiz 8: Interval Estimation

You are given the following information obtained from a random sample of 5 observations taken from a large population. Construct a 95% confidence interval for the mean of the population, assuming the population has a normal distribution.

A random sample of 95 students at a local university showed that they work an average of 48 hours per month with a standard deviation of 12 hours.Compute a 95% confidence interval for the mean of the population.

A sample of 100 students from a large university was taken.The average age in the sample was 22 years with a standard deviation of 4 years.Construct a 95% confidence interval for the average age of the population.

A random sample of 144 checking accounts at a bank showed an average daily balance of $500 and a standard deviation of $60.Develop a 95% confidence interval estimate for the mean of the population.

If the population standard deviation of the lifetime of washing machines is estimated to be 1000 hours, how large a sample must be taken in order to be 95% confident that the margin of error will not exceed 100 hours?

The manager of a department store wants to determine the proportion of people who use the store's credit cards for their purchases.What sample size should he take so that, at 95% confidence, the error will not be more than 6%?

In a sample of 200 individuals, 130 indicated they are Democrats.Develop a 95% confidence interval for the proportion of Democrats in the population.

Quiz 8: Interval Estimation

You are given the following information obtained from a random sample of 5 observations taken from a large population. ​ Construct a 95% confidence interval for the mean of the population, assuming the population has a normal distribution.

A random sample of 95 students at a local university showed that they work an average of 48 hours per month with a standard deviation of 12 hours.Compute a 95% confidence interval for the mean of the population.

A sample of 100 students from a large university was taken.The average age in the sample was 22 years with a standard deviation of 4 years.Construct a 95% confidence interval for the average age of the population.

A random sample of 144 checking accounts at a bank showed an average daily balance of $500 and a standard deviation of $60.Develop a 95% confidence interval estimate for the mean of the population.

If the population standard deviation of the lifetime of washing machines is estimated to be 1000 hours, how large a sample must be taken in order to be 95% confident that the margin of error will not exceed 100 hours?

The manager of a department store wants to determine the proportion of people who use the store's credit cards for their purchases.What sample size should he take so that, at 95% confidence, the error will not be more than 6%?

In a sample of 200 individuals, 130 indicated they are Democrats.Develop a 95% confidence interval for the proportion of Democrats in the population.

You are given the following information obtained from a random sample of 5 observations taken from a large population. Construct a 95% confidence interval for the mean of the population, assuming the population has a normal distribution.