Chapter 4 Practice Test 1 A

The History Test had a national mean of µ = 52 and a standard deviation of σ = 9. Use the z for a sample mean formula to determine the probability that a random sample of 27 students will have a mean test score of 56 or greater.

.01

The History Test had a national mean of µ = 52 and a standard deviation of σ = 9. How much sampling error would you expect for a sample with a size of 27?

1.73

An honors history instructor and an honors statistics instructor had a friendly rivalry. They wanted to compare the mean performance of the honors history class to the mean performance of the honors statistics class. The mean score of the 27 students in the history class on the standardized History Test was 56. The national mean (i.e., µ) and standard deviation (i.e., σ) for the History Test was 52 and 9, respectively. Compute the z for a sample mean for the History test.

2.31

The mean score of the 18 students in the statistics class on the standardized Statistics Test was 75. The national mean (i.e., µ) and standard deviation (i.e., σ) for the Statistics Test was 69 and 10, respectively. Compute the z for a sample mean for the Statistics test.

2.55

A psychologist would like to determine if there is a relationship between depression and aging. It is known that the general population averages μ = 40 on a standardized depression test. The psychologist obtains a sample of n = 36 individuals who are all over the age of 70. The average depression score for this sample is 44.5 with a standard deviation of 11. Compute the 95% confidence interval around the difference between the sample mean and the population mean using the t formula. What is the margin of error (MOE) for this confidence interval?

3.72

A psychologist would like to determine if there is a relationship between depression and aging. It is known that the general population averages μ = 40 on a standardized depression test. The psychologist obtains a sample of n = 36 individuals who are all over the age of 70. The average depression score for this sample is 44.5 with a standard deviation of 11. Compute the 95% confidence interval around the difference between the sample mean and the population mean using the t formula. What is the point estimate for the confidence interval around the mean difference?

4.5

The mean score of the 18 students in the statistics class on the standardized Statistics Test was 75. The national mean (i.e., µ) and standard deviation (i.e., σ) for the Statistics Test was 69 and 10, respectively. Compute the 95% confidence interval around the difference between the sample mean and the population mean using the z. What is the margin of error (MOE) for this confidence interval?

4.62

The mean score of the 18 students in the statistics class on the standardized Statistics Test was 75. The national mean (i.e., µ) and standard deviation (i.e., σ) for the Statistics Test was 69 and 10, respectively. Compute the 95% confidence interval around the difference between the sample mean and the population mean using the z. What is the point estimate for this confidence interval?

6

How is the standard error influenced by sample size?

As sample size increases, the standard error decreases

According to the central limit theorem what shape do distributions of sample means tend to take?

Distributions of sample means tend to be normally distributed (bell-shaped)

Which of the following is the best interpretation of the confidence interval computed above?

It is a range of plausible estimates of the mean difference between the honor students and the population

A psychologist would like to determine if there is a relationship between depression and aging. It is known that the general population averages μ = 40 on a standardized depression test. The psychologist obtains a sample of n = 36 individuals who are all over the age of 70. The average depression score for this sample is 44.5 with a standard deviation of 11. Compute the confidence interval around the difference between the sample mean and the population mean using the t formula.

LB = .78, UB = 8.22

The mean score of the 18 students in the statistics class on the standardized Statistics Test was 75. The national mean (i.e., µ) and standard deviation (i.e., σ) for the Statistics Test was 69 and 10, respectively. Compute the 95% confidence interval around the difference between the sample mean and the population mean using the z.

LB = 1.38, UB = 10.62

The central limit theorem describes three important properties of all distributions of sample means of any given sample size. What are the three properties it describes? Select all that apply.

Shape Central Tendency Variability

Which honors class did better on their respective standardized test?

Statistics

You are interested in studying self-esteem among college students and plan to obtain a sample of 36 students from the population. The self-esteem questionnaire you plan to use has a mean of 90 and a standard deviation of 12. Which of the following best describes the distribution of sample means?

The collection of all possible random samples of 36 students will have a mean of 90 and a standard deviation of 2.

According to the central limit theorem what is the standard deviation of all distributions of sample means going to equal? Select all that apply.

The standard error of the mean σ /√N

The History Test had a national mean of µ = 52 and a standard deviation of σ = 9. Which is more likely to occur:

drawing a random sample of 27 students from the national population of high school students that has a mean equal to or greater than 56

In general, the _______________ sample size, the closer the shape of the distribution of sample means is to a normal distribution

larger

The standard error is a measure of

sampling error

Scores on a memory test are normally distributed with a mean of μ = 100 in the general population. A teacher wonders how the memory scores of students in advanced placement classes compare to the general population. To test this, he obtains a random sample of 25 students in advanced placement classes and gives them the memory test. He computes the mean (105) and the standard deviation (15.3) for these 25 students. Which statistic should he use to compute the probability of obtaining a sample mean of 105 or higher with a sample size of 25?

single sample t

Scores on an intelligence test are normally distributed in the population with a mean of 100 and a standard deviation of 15. A grade school principal wonders if the children in her school are above or below average. To investigate this she takes a random sample of 45 children and has a psychologist administer an IQ test. The mean in the school was 95. What statistic should she use to determine the probability of a randomly selected sample of 45 children from the population having a mean of 95 or lower?

z for a sample mean

Scores on the ACT are normally distributed with a mean of 21 and a standard deviation of 5.4. A student knows that her score on the ACT was 24. What statistic should she use to determine what percent of students did better than her on the ACT?

z for a single score

The weights of one year old girls are normally distributed with a mean of 19 lbs 10 ounces with a standard deviation of 2 lbs. A parent is concerned that her one year old daughter is very small for her age because she weighs just 17 pounds. What percent of one year old girls weigh 17 pounds or less? What statistics should you use to answer this question?

z for a single score

According to the central limit theorem what is the mean of all distributions of sample means going to equal?

μ