stat200 week 5 homework

First set Chap8 # 100, 106, 112, 116, 120, 130 & Second set Chapt10 # 4, 12, 15, 18

Question 1 David Lane: Page 364 Exercise 4

Why is a 99% confidence interval wider than a 95% confidence interval?

Answer:

Question 2 David Lane: Page 365 Exercise 15

You take a sample of 22 from a population of test scores, and the mean of your sample is 60.

You know the standard deviation of the population is 10.

What is the point estimate for the population mean?

What is the 99% confidence interval on the population mean?

Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10.

What is the 99% confidence interval on the mean now?

What distribution did you use when computing the first confidence interval?

What is the degrees freedom for calculating the confidence interval?

What distribution did you use when computing the second confidence interval?

What is the degrees freedom for calculating the confidence interval?

Question 3 David Lane: Page 366 Exercise 18

You were interested in how long the average psychology major at your college studies per night, so you asked 10 psychology majors to tell you the amount they study.

You were given the following study times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4.

The average study time from the above data (Xbar)

The standard deviation of the study times from the above data

What is the appropriate distribution for finding a confidence interval?

What is the degrees of dreedom (dF)?

Find the 95% confidence interval on the population mean.

Find the 90% confidence interval on the population mean.

Question 4 Illowsky: Page 450 Exercise 100

What is meant by the term “90% confident” when constructing a confidence interval for a mean?

Question options:

· If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

· If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.

· If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

· If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

Question 5 Illowsky: Page 452 Exercise 106

Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours.

i. x ¯ = 8

ii. Standard deviation = 4

iii. n = 81

iv. n – 1 = 81 – 1 = 80

Define the random variables X and X ¯ by selecting the appropriate letter below.

Which distribution should you use for this problem?

Enter the degrees of freedom for this problem

Construct a 95% confidence interval for the population mean time wasted.

What is meant by the term “95% confident” when constructing a confidence interval for a mean?

Question 6 Illowsky: Page 454 Exercise 112

In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156.

Assume the underlying distribution is approximately normal.

Which distribution should you use for this problem?

Enter the degrees of freedom (dF) for this problem

Define the random variables X and X ¯ by selecting the appropriate letter below.

Construct a 95% confidence interval for the population mean time wasted.

What is meant by the term “95% confident” when constructing a confidence interval for a mean?