Understanding Stats Practice Exam 3

A particular psychological test is used to measure need for achievement. The average test score for all university students in Oklahoma is 115. A university in southern Oklahoma estimates the mean test score for a sample of n students to be 110 and constructs a confidence interval based on their scores. Which of the following statements about the confidence interval is always true? A. The resulting interval will contain 115. B. The 95% confidence interval for n = 100 will be more narrow than the 95% confidence interval for n = 50. C. For n = 100, the 95% confidence interval will be wider than the 90% confidence interval. A only A & B C only A & C B & C All three are true

B & C

In a recent study of Vietnam veterans, researchers found that among the population of veterans, .37 have been divorced at least once. If I took all possible samples of size n= 35 from this population, calculated the sample proportion on each sample, and arranged the sample proportions into a frequency distribution, the standard deviation of this sampling distribution would equal ______. a. 0.63 b. 0.08 c. 0.37 d. 0.06

b. 0.08

A 95% confidence interval indicates that: a. 95% of the time, the interval will include the sample mean. b. 95% of the intervals constructed using this process based on samples from the population will include the population mean. c. 95% of the possible population means will be included within the interval. d. 95% of the possible sample means will be included within the interval.

b. 95% of the intervals constructed using this process based on samples from the population will include the population mean

Other things being equal, as the sample size increases, the standard error of a statistic ______. a. Approaches the standard deviation of the population b. Decreases c. Remains constant if the value of sigma is known. d. Increases e. Approaches the population mean in numerical value

b. Decreases

Suppose that an organization is concerned about the number of its new employees who leave the company before they finish one year of work. In an effort to predict whether a new employee will leave or stay, the organization develops a standardized test and applies it to 100 new employees. After one year, they note what the test had predicted (stay or leave) and whether the employee actually stayed or left. They then compiled the data into the following table: Actually Stays Actually Leaves Total Predicted to Stay 63 12 75 Predicted to Leave 21 4 25 Total 84 16 100 It is __________ that an employee predicted to leave will actually leave as it is for one who is predicted to stay to actually leave. a. More likely b. Equally likely c. Less likely

b. Equally likely

The amount of time it takes to take an exam has a negatively (left) skewed distribution with a population mean of 65 minutes and a standard deviation of 8 minutes. A sampling distribution of the mean for n = 64 will: a. Have a mean of 65, a standard deviation of 1, and be negatively (left) skewed in shape. b. Have a mean of 65, a standard deviation of 1, and be normal in shape. c. Have a mean of 0, a standard deviation of 1, and be negatively (left) skewed in shape. d. Have a mean of 65, a standard deviation of 8, and be normal in shape.

b. Have a mean of 65, a standard deviation of 1, and be normal in shape.

If the occurrence of one event does not influence the outcome of another event, then the two events are: a. Interdependent b. Independent c. Mutually Exclusive d. Conditional

b. Independent

In which of the following situations would the gambler's fallacy not apply? A. When the events are not independent. B. When knowledge of one outcome affects the probability of the next one. a. It would not apply in situation B. b. It would not apply in neither situation A nor situation B. c. It would apply in both situations A and B. d. It would not apply in situation A.

b. It would not apply in neither situation A nor situation B.

If you take all samples of a particular size from a selected population, find the mean of each sample, and then plot the means, what have you created? a. Sample distribution b. Sampling distribution c. Population distribution d. Statistic distribution e. Parameter distribution

b. Sampling distribution

Which of the following is an example of the availability heuristic? a. Believing that a warranty plan that completely covers 30% of the possible problems is a better deal than a plan that covers 30% of all possible problems. b. Thinking that you won't get lung cancer if you smoke because you know many smokers and none of them have lung cancer. c. Thinking that events with more detailed descriptions are more likely than events with very general descriptions. d. Believing that random events are self-correcting (i.e. if you are on a losing streak, believing that your luck is about to turn around)

b. Thinking that you won't get lung cancer if you smoke because you know many smokers and none of them have lung cancer.

The amount of money college students spend each semester on textbooks is normally distributed with a mean of $250 and a standard deviation of $30. Suppose you take a random sample of 100 college students from this population. There would be a 68% chance that the sample mean (𝑥̅) amount spent on textbooks would be between: a. $220 and $280 b. $235 and $265 c. $247 and $253 d. $190 and $310

c. $247 and $253

A refrigerator contains 50 pieces of fruit: 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 8 mangos.Imagine that you put your hand in the refrigerator and pull out a piece of fruit. You decide you do not want to eat that fruit, so you put it back into the refrigerator and pull out another piece of fruit. What is the probability that you will pull a banana on the first try and an apple on the second try? a. 0.32 b. 0.2 c. 0.024 d. 0.5 e. 0.12

c. 0.024

A random sample of 121 students from the University of Oklahoma had a sample mean ACT score of 23.4 with a sample standard deviation of 3.65. Construct a 95% confidence interval for the population mean ACT score of University of Oklahoma students. a. 23.07 to 23.73 b. 19.75 to 27.05 c. 22.74 to 24.06 d. 16.1 to 30.7

c. 22.74 to 24.06

A small town has 3500 families. The population mean (mu) number of children per family is = 3, with a population standard deviation (sigma) = 0.60. A sampling distribution of the mean for n= 100 is developed for this population. What is the mean of this sampling distribution? a. 35 b. 0.60 c. 3 d. 0.06

c. 3

If you flip a fair coin and get heads 5 times in a row, what is the probability of getting tails on the next flip? a. Less than 50% b. Greater than 50% c. 50%

c. 50%

Which of the following is a property of the sampling distribution of 𝑥̅? a. 𝑥̅ always has a normal distribution. b. The standard deviation of the sample mean is the same as the standard deviation of the original population (sigma). c. The mean of the sampling distribution of 𝑥̅ is the population mean (mu). d. If you increase your sample size, 𝑥̅ will always get closer to the population mean (mu)

c. The mean of the sampling distribution of 𝑥̅ is the population mean (mu).

A 2018 sample of 130 college students randomly selected from a university indicated that 91 were sexually active.The researcher calculated a 95% confidence interval for the data to be .62 to .78. If the researcher had created a 99.7% confidence interval instead, the interval would have been: a. Narrower b. The same width c. Wider

c. Wider

An insurance company writes policies for 500 newly-licensed drivers each year. Suppose 45% of these are low-risk drivers, 45% are moderate-risk, and 10% are high risk. The company has no way to know which group any individual driver falls in when it writes the policies. None of the low-risk drivers will have an at-fault accident in the next year, but 20% of the moderate-risk and 30% of the high-risk drivers will have an at-fault accident. Given that a driver has an at-fault accident in the next year, what is the probability that he or she is high-risk? (Hint: use your percentages to create a table with risk level as your columns and fault/no-fault accidents as your rows, and 500 as your total number of people in the table.) a. 0.03 b. 0.75 c. 0.30 d. 0.25

d. 0.25

Which of the following statements is not true regarding a 95% confidence interval for the mean of a population? a. In 95% of all samples, the true population mean will be within 2 standard errors of the sample mean. b. If you add and subtract two standard errors to and from the sample mean, in 95% of all cases, you will have captured the true population mean. c. In 95% of all samples, the sample mean will fall within 2 standard errors of the true population mean. d. 95% of the population values will lie within 2 standard errors of the sample mean.

d. 95% of the population values will lie within 2 standard errors of the sample mean.

The table below is based on records of accidents in 1988 compiled by the Department of Highway Safety and Motor Vehicles in the state of Florida. Nonfatal Injury Fatal Injury Total Seat Belt Worn 412,368 510 412,878 No Seat Belt Worn 132,527 4,601 137,128 Total 544,895 5,111 550,006 What is the probability of someone having a nonfatal accident given that no seatbelt was worn? a. 24.1% b. 99.1% c. 24.3% d. 96.6% e. 28.3%

d. 96.6%

Beth and Kathy worked together to estimate the proportion of college students who say they drink alcohol of one kind or another.They collect a random sample of 50 college students and calculate a sample proportion of students who say they drink alcohol to be .78. They each create a 95% confidence interval for their finding. Beth's 95% confidence interval is .74 to .88, while Kathy's 95% confidence interval is .72 to .84. Which of the following statements is correct? a. Kathy's confidence interval must be incorrect, because the sample proportion is not exactly in the middle of her confidence interval. b. Both Beth's and Kathy's confidence interval can be correct, because they may have calculated different standard deviations which gave them different intervals. c. Neither Beth's nor Kathy's confidence interval can be correct, because the sample proportion is not one of the interval's end points. d. Beth's confidence interval must be incorrect, because the sample proportion is not exactly in the middle of her confidence interval.

d. Beth's confidence interval must be incorrect, because the sample proportion is not exactly in the middle of her confidence interval.

If sampling distributions of sample means are examined for samples of size 2, 16, and 50, you will notice that as n increases in size, the shape of the sampling distribution appears more like that of the: a. Skewed distribution b. Population distribution c. Uniform distribution d. Normal distribution

d. Normal distribution

If a fair die is rolled five times, which of the following ordered sequence of result, if any, is most likely to occur? A. 3 5 1 6 2 B. 4 2 6 1 5 C. 5 2 2 2 2 a. A b. Sequences (A) and (B) are equally likely c. B d. Sequences (A), (B), and (C) are all equally likely e. Sequences (B) and (C) are equally likely f. C

d. Sequences (A), (B), and (C) are all equally likely

Given that the probability of having a boy or girl is p = 0.50, which probability is the smallest? a. The probability that a couple's third child is a girl. b. The probabilities of the three other choices are all equal. c. The probability that at least one of a couple's 3 children is a girl. d. The probability that a couple's first girl occurs the third time around (so the couple has a boy and then another boy and then a girl).

d. The probability that a couple's first girl occurs the third time around (so the couple has a boy and then another boy and then a girl).

Researchers were interested in the population proportion of undergraduate students at the University of Oklahoma who are from the state of Oklahoma. They took a random sample of 200 students and found that 170 of them are from Oklahoma. They calculated a 95% confidence interval for the population proportion p to be .8 to .9. What would you estimate the standard error of the proportion to be? a. 0.025 b. 0.1 c. 0.05 d. 0.15

a. 0.025

Suppose the population proportion of American citizens who are in favor of gun control is .61. If a sampling distribution of size n= 50 was created from this population, what would be the mean of this sampling distribution? a. 0.61 b. 0.07 c. 0.06 d. 0.39

a. 0.61

Suppose Disease X occurs in 14% of a population with a total of 250,000 people. A test for Disease X has a sensitivity of 92% and a specificity of 94%. What is the probability that you actually have the disease given that your test results are positive (i.e. the test indicates that you have the disease)? Complete the table below to help you determine the answer. Have Disease Don't Have Disease Total Positive Negative Total 250,000 a. 0.71 b. 0.63 c. 0.13 d. 0.14 e. 0.94 f. 0.92

a. 0.71

The standard error of the mean is a name for the standard deviation of the: a. Sampling distribution of the mean b. Sample c. Population d. Raw scores e. Sampling distribution of the variance

a. Sampling distribution of the mean

Suppose there is a population of test scores on a large, standardized exam for which the mean and standard deviation are unknown. Two different random samples of 50 data values are taken from the population. One sample has a larger sample standard deviation (SD) than the other. Each of the samples is used to construct a 95% confidence interval. How do you think these two confidence intervals would compare? a. The confidence interval based on the sample with the larger standard deviation would be wider. b. The two confidence intervals would have the same width because they are both 95% confidence intervals. c. The confidence interval based on the sample with the smaller standard deviation would be wider. d. The two samples would produce identical values for the lower and upper bounds of the two confidence intervals.

a. The confidence interval based on the sample with the larger standard deviation would be wider.

Which of the following values will always be within the upper and lower limits of the confidence interval? a. The sample mean b. The population mean c. The sample size d. The standard deviation of the sample

a. The sample mean