Psych 300 Ch. 4

A scientist collected a sample of data of cactus heights. The data was rounded to the nearest half foot. If the minimum score was 3.5 feet and the range was 4 feet, what was the maximum score? a. 7.25 feet b. 7 feet c. 7.5 feet d. 8 feet

b. 7 feet The real lower limit for 3.5 feet is 3.25 feet. The real upper limit of the set of scores will be 3.25 + 4 = 7.25 feet. So the maximum score will be 7 feet.

A teacher has given a test to a group of students. The set of scores is: 78, 79, 79, 81, and 83. Find the sample variance for this group of tests scores. a. 2.24 b. 3.4 c. 4 d. 80

c. 4

Under what circumstances would a score that is below the mean by 3 points appear to be very far from the mean? a. When the mean is much greater than 3 b. When the standard deviation is much greater than 3 c. When the standard deviation is much less than 3 d. When the mean is much less than 3

c. When the standard deviation is much less than 3 If the standard deviation is much less than 3, then a score 3 points below the mean would be many standard deviations away from the mean, and would therefore appear very far away from the mean.

An unbiased statistic is one in which ... a. the average value of the statistic is greater than the population parameter. b. the average value of the statistic is less than the population parameter. c. the average value of the statistic is equal to the population parameter. d. the average value of the statistic is either greater than or less than the population parameter.

c. the average value of the statistic is equal to the population parameter

A researcher selects all of the possible samples with n = 7 scores from a population and computes the sample variance, dividing by n - 1, for each sample. If the population variance is σ2 = 9, then what is the average value for all of the sample variances? a. 9 b. greater than 9 c. less than 9 d. impossible to determine

A. 9 Sample variance using n - 1 is an unbiased statistic, so the average value of all sample variances will be the same as the population variance, or 9

When is the standard deviation of a set of scores equals to 0? a. when the range of the scores is 0 b. when there are only two scores in the set c. The standard deviation is never 0. It is always positive. d. when the variance of the scores is negative

A. When the range of the scores is 0

The following is a sample of IQs from a population. Find the sample standard deviation to two decimal places. 105 107 107 120 122 147 a. 212.17 b. 15.95 c. 14.57 d. 254.4

B. 15.95

A sample has five scores, but only four of them are known. However, the sample standard deviation is s = 3, and the mean is M = 4. If the four known scores are 1, 1, 5, and 8, which is a possibility for the fifth score? 1. 3 2. 4 3. 5 a. I and III b. III only c. II only d. I only

B. III only If s = 3, then s 2 = 9. Since , 9 = SS/4. Therefore, SS = 36. Four of the squared deviations are known: (1 - 4)2, (1 - 4)2, (5 - 4)2, and (8 - 4)2. So 36 = 35 + (x - 4)2, where x is the missing score. x = 3 or 5 solves this. However, the mean is M = 4, which holds true only when the fifth score is x = 5.

Which of the following sets of scores has the least variability? a. 5, 7, 8, 9, 12, 13 b. 16, 17, 18, 19, 20 c. 1, 2, 3, 10, 11, 12 d. 20, 22, 25, 30,31

b. 16, 17, 18, 19, 20

What is the range for the set of scores: 7, 8, 11, 15, 17, 20? a. 7 b. 1 or 2 c. 13 or 14 d. 20

C. 13 or 14

In the context of inferential statistics, the variance that exists in a set of sample data is often classified as a. standard deviation b. bimodal variance c. mean variance d. error variance

D. error variance

A researcher was asked to provide the standard deviation for a sample of fish weights. The researcher originally reported a standard deviation of 12.3 grams. However, upon closer investigation, she discovered that her scale was 1.1 grams off, and that each fish was actually 1.1 grams heavier than originally reported. What is the new standard deviation? a. 12.3 b. 13.4 c. 15.53 d. It is impossible to tell without knowing the original weights.

a. 12.3 When the scores in a sample are increased by the same amount, the standard deviation is unchanged, so the new standard deviation is the same as the original standard deviation, 12.3

A researcher selects all of the possible samples with n = 8 scores from a population and computes the mean, dividing by n, for each sample. If the population mean is μ= 14, then what is the average value for all of the sample means? a. 14 b. greater than 14 c. less than 14 d. impossible to determine

a. 14

Which of the following is a true statement? a. Samples tend to be less variable than their populations. b. Samples tend to be more variable than their populations. c. Samples and their populations tend to have the same variability. d. None of the above is true.

a. Samples tend to be less variable than their populations

Which of the following is true for the quantity ∑(X - μ)? a. This is the sum of the deviations, and it is always 0. b. This is the variance, and it is sometimes positive. c. This is the variance, and it is always positive. d. This is the standard deviation, and it is always positive.

a. This is the sum of the deviations, and it is always 0. ∑(X - μ) is the sum of the deviations from the mean. Because the mean is the balance point of a set of scores, the sum of the deviations is always 0

Each score in a set of data is multiplied by 5, and then 7 is added to the result. If the original mean is 8 and the original standard deviation is 2, what are the new mean and new standard deviation? a. μ = 40, σ = 10 b. μ = 47, σ = 9 c. μ = 47, σ = 10 d. μ = 47, σ = 17

c. μ = 47, σ = 10 When the scores are multiplied by a constant, both the mean and the standard deviation are multiplied by the constant. When the scores are increased by a number, the mean is increased by that number, but the standard deviation is not changed. So the new mean is 8 × 5 + 7 = 47, but the new standard deviation is 2 × 5 = 10.

A scientist collects a sample of honeybees from a hive. He weighs the honeybees in grams and calculates the standard deviation to be 0.002 grams. If there are 1000 milligrams in one gram, what is the standard deviation in milligrams? a. 0.02 b. 0.002 c. 0.0002 d. 2

d. 2 If the scores in a sample of data are multiplied by a constant, then the standard deviation is multiplied by that same constant. So the original standard deviation would be multiplied by 1000 to get 2 milligrams.

When is the population standard deviation greater than the population variance? a. when the variance is negative b. when the variance is greater than 1 c. The standard deviation is never greater than the variance. d. when the variance is less than 1

d. when the variance is less than 1

Find the population variance and standard deviation for the following ages of children in a family: 1, 3, 5, 7, 8, 11, 14. a. σ = 17.43, σ2= 4.17 b. σ = 122, σ2= 11.05 c. σ = 11.05, σ2= 122 d. σ = 4.17, σ2= 17.43

d. σ = 4.17, σ2= 17.43