Question 1

A random sample of 121 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $44. Develop a 95% confidence interval estimate for the mean of the population.

Accepted Answer

The answer of A random sample of 121 checking accounts...

Question 2

In a sample of 200 individuals, 120 indicated they are Democrats. Develop a 95% confidence interval for the proportion of people in the population who are Democrats.

Accepted Answer

The answer of In a sample of 200 individuals, 120...

Question 3

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.

Accepted Answer

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

Question 4

Choo Choo Paper Company produces papers of various thickness. A random sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils. Develop a 95% confidence interval for the mean thickness of the population.

Accepted Answer

The answer of Choo Choo Paper Company produces papers of...

Question 5

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 a 80% confidence interval estimates for the mean.
e.Construct a 95% confidence interval for the mean.

Accepted Answer

The answer of A random sample of 121 checking accounts...

Question 6

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 $\mu$.
b.Construct a 99% confidence interval for $\mu$.
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.

Accepted Answer

The answer of A random sample of 53 observations was...

Question 7

You are given the following information obtained from a sample of 5 observations taken from a population that has a normal distribution.
94 72 93 54 77
Develop a 98% confidence interval estimate for the mean of the population.

Accepted Answer

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

Question 8

A sample of 60 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.

Accepted Answer

The answer of A sample of 60 students from a...

Question 9

A sample of 144 cans of coffee showed an average weight of 16 ounces. The standard deviation of the population is known to be 1.4 ounces.
a.Construct a 68.26% confidence interval for the mean of the population.
b.Construct a 97% confidence interval for the mean of the population.
c.Discuss why the answers in Parts a and b are different.

Accepted Answer

The answer of A sample of 144 cans of coffee...

Question 10

It is known that the variance of a population equals 1296. A random sample of 144 observations is going to be taken from the population.
a.With a 0.95 probability, what statement can be made about the size of the margin of error?
b.With a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 6 or less?

Accepted Answer

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

Question 11

You are given the following information obtained from a random sample of 5 observations taken from a large population. 32 34 32 30 32
Construct a 95% confidence interval for the mean of the population, assuming the population has a normal distribution.

Accepted Answer

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

Question 12

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 13

Two hundred students are enrolled in an Economics class. After the first examination, a random sample of 6 papers was selected. The grades were 65, 75, 89, 71, 70 and 80.
a.Determine 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 95% confidence interval for the mean grade of all the students in the class.

Accepted Answer

The answer of Two hundred students are enrolled in an...

Question 14

The average monthly electric bill of a random sample of 256 residents of a city is $90 with a standard deviation of $24.
a.Construct a 90% confidence interval for the mean monthly electric bills of all residents.
b.Construct a 95% confidence interval for the mean monthly electric bills of all residents.

Accepted Answer

The answer of The average monthly electric bill of a...

Question 15

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.

Accepted Answer

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

Question 16

A random sample of 49 lunch customers was taken at a restaurant. The average amount of time the customers in the sample 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?

Accepted Answer

The answer of A random sample of 49 lunch customers...

Question 17

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. He reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. He neglected to report what confidence coefficient he had used. Based on the above information, determine the confidence coefficient that was used. Assume the population has a normal distribution.

Accepted Answer

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

Question 18

A random sample of 81 students at a local university showed that they work an average of 60 hours per month with a standard deviation of 18 hours. Compute a 95% confidence interval for the mean of the population.

Accepted Answer

The answer of A random sample of 81 students at...

Question 19

Many people who bought X-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 18 units were defective.
a.Determine a 95% confidence interval for the percentage of defective systems.
b.If 1.5 million X-Games were sold over the holidays, determine an interval for the number of defectives in sales.

Accepted Answer

The answer of Many people who bought X-Game gaming systems...

Question 20

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.

Accepted Answer

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

Quiz 8: Interval Estimation