STATS Review

Deanna is the principal at a Midwestern middle school and she wants to know the average IQ of all female, seventh-grade students in the school. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Assuming that the Central Limit Theorem conditions are met, what is the 98% confidence interval for the true average IQ score of all seventh-grade girls in this school? A. (99.523, 112.077) B. (104.182, 107.418) C. (103.475, 108.126) D. (100.520, 111.080) E. (99.181, 112.419)

A. (99.523, 112.077)

Suppose you have calculated a confidence interval with a certain percentage of confidence and sample size. What would happen to the width of the interval if we increase the sample size and decrease the percentage of confidence? A. It would decrease. B. It would stay the same. C. It is impossible to determine. D. It would increase.

A. It would decrease.

As the sample size increases, what happens to the shape of the sampling distribution of -x? A. It becomes closer to the population distribution. B. It becomes closer to a normal distribution. C. It is impossible to tell what will happen. D. It does not change. E. It becomes more skewed.

B. It becomes closer to a normal distribution.

Suppose that adult women in China have heights that are normally distributed with a mean of 155 centimeters and a standard deviation of 8 centimeters and that adult women in Japan have heights that are normally distributed with a mean of 158 centimeters and a standard deviation of 6 centimeters. Which country has the higher percentage of women taller than 165 centimeters? A. The percentages are the same. B. Japan C. China D. It is not possible to tell from the information given.

B. Japan

Use the following information for questions 16-17: A person's blood pressure is monitored by taking 5 readings daily. Suppose the probability distribution of his readings is normal with a mean of 130 and a standard deviation of 6. What is the probability that the sample mean exceeds 135? Hint: First find the mean and the standard deviation of the sampling distribution. A. 1.86 B. 0.9686 C. 0.0314 D. 3.14 E. 0.2033

C. 0.0314

As a part of a class project in this course, suppose we are interested in knowing the average cholesterol level of all women between the ages of 21 and 30 who live in College Station. Everyone in this class (about 100 students) takes a random sample of 50 females in the College Station area between the ages of 21 and 30, and then records their cholesterol levels. Each student also calculates the average cholesterol level based on their sample. Suppose you make a histogram of the 50 cholesterol levels that you have sampled. Which of the following distributions does your histogram display? A. Population Distribution B. Sampling Distribution C. Data Distribution D. More than one of the above E. None of the above

C. Data Distribution

Suppose the US presidential election is in a few months and a Gallop poll wants to determine the proportion of people who plan on voting for neither the republican nor the democratic candidate in the upcoming election (that is, they will vote for a third party). They conduct a random phone poll, where they contact 500 individuals and ask them whether or not they plan on voting for a third-party candidate. Of these 500 respondents, 35 people say they plan on doing so. The 90% confidence interval for this scenario is (0.0513, 0.0888). What is the correct interpretation of the 90% confidence interval? A. We are confident that 90% of people will vote for between 5.13% and 8.88% of third-party candidates. B. We are confident that between 5.13% and 8.88% of people will vote for a third-party candidate 90% of the time. C. We are 90% confident that the true proportion of people who plan on voting for a third party in the upcoming election is between 0.0513 and 0.0888. D. There is a 90% chance that the proportion of people who will vote for a third party candidate is between 0.0512 and 0.0888. E. We are 90% sure that the proportion of respondents who plan on voting third party in the upcoming election is between 0.0512 and 0.0888.

C. We are 90% confident that the true proportion of people who plan on voting for a third party in the upcoming election is between 0.0513 and 0.0888.

Use the following information for questions 10-11: One common disease among pediatric patients is streptococcal pharyngitis (strep throat). If a pediatric patient comes to the pediatricians feeling ill, there is a 26% chance that they have strep throat. A doctor sees 7 pediatric patients on a particular day. Assume these patients are independent. How many pediatric patients can the doctor expect to have strep throat? A. 2.00 B. 1.3468 C. 1.1605 D. 1.82 E. 182

D. 1.82

As the sample size decreases. what happens to the standard deviation of the sampling distribution of ^p? A. It does not change. B. It decreases. C. It is impossible to tell. D. It increases.

D. It increases.

Use the following information for questions 16-17: A person's blood pressure is monitored by taking 5 readings daily. Suppose the probability distribution of his readings is normal with a mean of 130 and a standard deviation of 6. Consider his/her 5 readings on a particular day as the sample. What is the shape of the sampling distribution of the sample mean? A. The shape of the distribution is unknown. B. The distribution is uniform. C. The distribution is skewed right. D. The distribution is normal. E. The distribution is skewed left.

D. The distribution is normal.

Use the following information for questions 10-11: One common disease among pediatric patients is streptococcal pharyngitis (strep throat). If a pediatric patient comes to the pediatricians feeling ill, there is a 26% chance that they have strep throat. A doctor sees 7 pediatric patients on a particular day. Assume these patients are independent. What is the chance that at least one of them has strep throat? A. 0.299 B. 0.122 C. 0.580 D. 0.420 E. 0.878

E. 0.878

A random sample of 50 marriage records in Contra Costa County in California yields a 95% confidence interval of 21.5 to 23.0 years of age for the average age at first marriage for women. Which of the following is the correct interpretation of this interval? A. If random samples of 50 records were repeatedly selected, then 95% of the time the sample mean age at first marriage for women would be between 21.5 and 23.0 years. B. 95% of the ages of first marriage for women in Contra Costa County are between 21.5 and 23.0 years. C. We can be 95% confident the sample mean is between 21.5 and 23.0 years. D. If we repeatedly sampled the entire population, then 95% of the time the population mean would be between 21.5 and 23.0 years. E. None of the above.

E. None of the above.

The table below shows the probability distribution of Educational Attainment for Americans 25 years and older in 2019, as reported by the Census Bureau. For this survey, individuals were asked what their highest level of education was. The potential responses were: no formal education (None), some education but no HS diploma (No HS Diploma), HS graduate (HS Diploma), some college education but no degree (Some College), Associate Degree (Assoc.), Bachelor's Degree (Bach), or a Bachelor's Degree plus an advanced degree (Bach+). They were also asked what their sex was; for this question the Census Bureau defined sex as a binary variable so the potential responses were male or female. What is the probability that a randomly selected person is female or has an advanced degree (Bach+)? a. 0.581 b. 0.653 c. 0.072 d. 0.725 e. 0.533 f. 0.139

a. 0.581

Bonus: Given the probabilities shown below, what is the P(A|A)? P(A) = 0.93 P(B) = 0.23 P(A⋂B) = 0.18 a. 1.000 b. 0.930 c. 0.783 d. 0.194 e. Impossible to Determine

a. 1.000

A researcher is interested in learning how often college students watch TV. They randomly select 500 college students and ask, "In the past seven days, how many days did you watch television?" The random variable X represents the number of days an individual watched television. The probability distribution below shows the results of the survey. What is the expected value of X? a. 5.44 b. 3.50 c. 28.0 d. 5.00 e. 6.00

a. 5.44

Which of the following is a reason why a researcher may choose to use a cluster sample? a. Because they want to learn about each of the different clusters separately. b. Because they already have the complete sampling frame. c. Because it is impossible or not feasible to take a simple random sample or because the researcher can not get a list of every individual in the population. d. Because they want to use a smaller sample size.

c. Because it is impossible or not feasible to take a simple random sample or because the researcher can not get a list of every individual in the population.

In a study by Swedish researchers (Occupational and Environmental Medicine 2002;59:517-522), 2410 women who had worked as hairdressers and given birth to children were compared to 3462 women from the general population who had given birth. The researchers only asked the women whether or not they were hairdressers and whether or not their children had a birth defect. The study found that the hairdressers had a slightly higher percentage of infants with a birth defect. In this study, income, health benefits, age, and insurance are all examples of what type of variable? a. Confounding Variable b. Numerical Variable c. Explanatory Variable d. Response Variable e. Categorical Variable

a. Confounding Variable

A researcher wants to determine if a new vaccine protects people from COVID-19 better than the current Moderna vaccine. She randomly selects 1000 subjects for her study. She believes that age will affect how well the vaccine works. So she splits these 1000 subjects into 10 disjoint age groups: 0 to 10, 10+ to 20, ..., 80+ to 90, and 90+ and above. The group of 1000 subjects that she started with is such that there are at least 20 subjects within each age group. Now within each age group, she randomly assigns half of the subjects to get the new vaccine and the other half to get the Moderna vaccine. What type of study design is this? a. Experimental Study: Block Design b. Observational Study: Simple Random Sample c. Experimental Study: Matched Pairs d. Observational Study: Stratified Random Sample e. Experimental Study: Completely Randomized Experiment

a. Experimental Study: Block Design

We know that the mean and median can be used to describe the centrality of distribution, and the IQR and standard deviation can be used to describe the spread of a distribution. When data is known to contain outliers (like below), which of the following combinations is the worst to determine its center and spread? a. Mean and Standard Deviation b. Median and Mean c. Median and IQR d. Median and Standard Deviation

a. Mean and Standard Deviation

Given the following situations, when would you use a histogram? a. Showing the distribution of the GPA's of all of the students at Texas A&M b. Showing the distribution of marital status for all of the adults in the United States c. Showing how the gender and disease status (whether or not someone has a disease) are related d. Showing how age and height are related for children in America e. Showing the grade distribution of the letter grades on an exam in an introductory statistics class

a. Showing the distribution of the GPA's of all of the students at Texas A&M

Suppose you called your local pharmacy to refill a prescription and are put on hold. Assume that the amount of time you will spend on hold is somewhere between 0 and 13 minutes and it follows a uniform distribution. What is the probability you will be on hold for exactly 8 minutes? a. 0.077 b. 0 c. 0.615 d. 0.385 e. Impossible to Determine

b. 0

Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have such a locator. Suppose that a light aircraft has disappeared. If it has an emergency locator, what is the probability that it will not be discovered? a. 0.93 b. 0.067 c. 0.45 d. 0.42 e. 0.61 f. 0.03 g. 0.69

b. 0.067

In your sock drawer you have 4 blue, 5 grey and 3 black socks. Half asleep one morning, you grab 2 socks at random and put them on. What is the probability you are wearing matching socks? a. 0.0006 b. 0.288 c. 0.264 d. 0.348 e. 0.091 f. 1

b. 0.288

A professional male basketball player is a poor free-throw shooter. Consider a situation in which he shoots a pair of free throws. Suppose, the probability that he makes the first free throw is 0.51, the probability that he makes the second one given that he makes the first is 0.59, and the probability that he makes the second one given that he misses the first is 0.36. What is the probability that he makes one of the two free throws? a. 0.2091 b. 0.3855 c. 0.6864 d. 0.9500 e. 0.1764

b. 0.3855

Use the following information for questions 28-31: A researcher wants to determine if there is an association between gender (only male and female are considered for ease) and the political party they prefer to vote. She interviewed 1000 random individuals and recorded their gender and their political party. The results are shown in the table below. Conduct the appropriate hypothesis test using a 0.05 significance level. What is the expected number of males who are independent? a. 133.33 b. 50 c. 40 d. 2.5 e. 133 f. 10

b. 50

Bonus: DeAnna wants to determine whether talking on the phone while driving is associated with more car accidents. What is the best way to design a study to see if there is a relationship between talking on the phone and traffic accidents? a. Non-Comparative Observational Study: Find a group of people who talk on the phone while driving and see how many accidents they have. b. Comparative Observational Study that Adjusts for Confounding Variables: Find a group of people who talk on the phone while driving and another group of people who don't, then see how many accidents each group of people get into and use adjustments as needed. c. She shouldn't study this. d. One-Track Experiment: Have all subjects in the experiment talk on the phone while driving and see how many accidents they have. e. Randomized Comparative Experiment: Randomly assign some people to talk on the phone while driving and others to not talk on the phone while driving and see which group of people has more accidents.

b. Comparative Observational Study that Adjusts for Confounding Variables: Find a group of people who talk on the phone while driving and another group of people who don't, then see how many accidents each group of people get into and use adjustments as needed.

Use the following information for questions 23-24: Suppose you conduct a hypothesis test to determine whether or not the average height of first grade students is less than 46 inches. You conduct this test at the 0.05 significance level and come to the conclusion that p-value = 0.07. What is the correct decision? a. Accept the Alternative Hypothesis b. Fail to Reject the Null Hypothesis c. Accept the Null Hypothesis d. Reject the Null Hypothesis

b. Fail to Reject the Null Hypothesis

Bonus: Given the probabilities shown below, are event A and event B independent? P(A) = 0.42 P(B) = 0.36 P(A⋃B) = 0.78 a. Impossible to Determine b. No c. Maybe d. Yes

b. No

Which of the following is an example of a voluntary response sample? a. Researcher splits their population into a group of a males and a separate group of females; she takes a random sample of 25 males and a separate random sample of 25 females b. Radio asks people listening to call in and say whether or not they want a new stoplight at a busy intersection c. Student asks 15 specific classmates to answer a survey about university fees d. Researcher at a major university randomly selects 50 students to participate in a survey. She sends the survey to the 50 selected students via email and 45 of them return the survey. e. More than one of the above

b. Radio asks people listening to call in and say whether or not they want a new stoplight at a busy intersection

Multiple myeloma is a cancer of the bone marrow currently without an effective cure. It primarily affects older individuals: It is almost never diagnosed in individuals under 40 years old, and its incidence rate (the number of diagnosed malignant cases per 100,000 individuals in the population) is highest among individuals 70 years of age and older. If you were to create a histogram to show the distribution of the incidence rate of multiple myeloma by age at diagnosis, how would you describe its skewness? a. Skewed Right b. Skewed Left c. Impossible to Determine d. Symmetric

b. Skewed Left

The following standardized stacked bar plot shows the relationship between the type of food (organic vs. conventional) and whether or not pesticides are present. Based on the graph, does it appear that there is an association between food type and pesticide status? a. Yes, because the conditional proportions are the same in both groups. b. Yes, because the conditional proportions are different in the two groups. c. No, because the conditional proportions are different in each group. d. No, because the conditional proportions are the same in each group.

b. Yes, because the conditional proportions are different in the two groups.

Suppose a researcher wants to test the hypothesis that p = 0.37 versus the alternative that p ≠ 0.37 using data from a random sample of 29 people. We calculate the standardized test statistic to be 1.84. Which of the following best describes the p-value? a. p-value = 0.0329 b. p value = 0.0658 c. p-value = 0.9671 d. 0.025 < p-value < 0.05 e. 0.05 < p-value < 0.10

b. p value = 0.0658

Use the following information for questions 4-6: Cholesterol levels for women ages 20-34 are approximately normally distributed with a mean of 185 mg/dL and a standard deviation of 39 mg/dL. Cholesterol levels between 200 mg/dL and 240 mg/dL are considered borderline high. What is the probability that a woman between the ages of 20 and 34 has a borderline high cholesterol level (that is, her cholesterol is between 200 mg/dL and 240 mg/dL)? a. 0.5454 b. 0.9207 c. 0.2727 d. 0.7273 e. 0.78435 f. 0.6480 g. 1.5687

c. 0.2727

Which of the below are the correct conditions for a binomial​ distribution? The n trials are independent. Each trial has at least two possible outcomes. The n trials are dependent. Each trial has the same probability of a success. There are two trials. Each trial has two possible outcomes. a. 2, 3, and 5 b. 1, 2, and 4 c. 1, 4, and 6 d. 3, 5 and 6 e. None of the above

c. 1, 4, and 6

Use the following information for questions 28-31: A researcher wants to determine if there is an association between gender (only male and female are considered for ease) and the political party they prefer to vote. She interviewed 1000 random individuals and recorded their gender and their political party. The results are shown in the table below. Conduct the appropriate hypothesis test using a 0.05 significance level. What is the chi-square contribution for male independents? a. 40 b. 10 c. 2.5 d. 0.25 e. -10 f. 16.3207

c. 2.5

Use the following information for questions 26-27: Rock-paper-scissors is a game played by two or more people where players choose either rock, paper, or scissors with their hands. For your statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. The following table summarizes the data: Under the assumption that no option is favored, what would the expected number of paper be? a. Impossible to determine b. 21 c. 20 d. 33 e. 0.33

c. 20

1380 randomly sampled registered voters from Tampa, Florida were asked if they thought workers who have illegally entered the US should be (i) allowed to keep their jobs and apply for US citizenship, (ii) allowed to keep their jobs as temporary guest workers but not allowed to apply for US citizenship, or (iii) lose their jobs and have to leave the country. The results of the survey by political ideology are shown below. Suppose a voter identifies as a conservative. Based on this data, what is the probability that the voter is in favor of the citizenship option? a. 6.3% b. 37.1% c. 20.0% d. 31.5% e. 17.0%

c. 20.0%

In which of the following study designs would you generally know the value of the parameter? a. Experiment b. Sample Survey c. Census d. More than one of the above e. None of the above

c. Census

The American Heart Association (AHA) reports that 4.9% of adolescents aged 12-17 are current smokers. Suppose you take a random sample of 100 adolescents between the ages of 12 and 17 and find that 3.2% are current smokers. Assuming the proportion reported by AHA is correct, what are the mean and the standard deviation of the sampling distribution of p̂? a. Mean: 0.049, Standard Deviation: 1.221 b. Mean: 0.049, Standard Deviation: 0.0382 c. Mean: 0.049, Standard Deviation: 0.0216 d. Mean: 4.9, Standard Deviation: 1.221 e. Mean: 0.032, Standard Deviation: 1.221

c. Mean: 0.049, Standard Deviation: 0.0216

For the distribution shown below, which point represents the mean and which point represents the median? a. It is impossible to tell from the given information b. Mean: Point B, Median: Point A c. Mean: Point B, Median: Point B d. Mean: Point A, Median: Point B e. Mean: Point C, Median: Point A

c. Mean: Point B, Median: Point B

A researcher wants to know more about the resting pulse rate of high school aged children. She takes a random sample of 17 students at a local high school and measures their resting pulse rate. The boxplot below depicts the five number summary for her data set. Based on this boxplot, what is the skewness of the data set? a. Skewed Left b. Symmetric c. Skewed Right d. Impossible to Determine

c. Skewed Right

Use the following information for questions 23-24: Suppose you conduct a hypothesis test to determine whether or not the average height of first grade students is less than 46 inches. You conduct this test at the 0.05 significance level and come to the conclusion that p-value = 0.07. What is the appropriate conclusion? a. The data does not provide statistically significant evidence that the average height of first grade students is 46 inches. b. The data does provide statistically significant evidence that the average height of first grade students is 46 inches. c. The data does not provide statistically significant evidence that the average height of first grade students is less than 46 inches. d. The data does provide statistically significant evidence that the average height of first grade students is less than 46 inches.

c. The data does not provide statistically significant evidence that the average height of first grade students is less than 46 inches.

A certain region has a population of 6.5 million. On any given day (excluding days like today where there is a pandemic and we aren't supposed to leave our houses), the probability that a randomly selected resident decides to visit the amusement park is 1/5000. Assume that each resident's decision to visit is independent of the other residents. What is the probability that all the residents of this region will decided to go to the amusement park tomorrow (assuming the amusement park is open tomorrow)? a. Very close to one b. Exactly equal to zero c. Very close to zero d. Exactly equal to one e. A very large number

c. Very close to zero

A professional basketball player has an 81% success rate when shooting free throws. Let the random variable X represent the number of free throws she makes in a random sample of 10 free throws (assume this experiment meets all requirements for the binomial distribution). What is the probability that he makes exactly 7 of the 10 free throws? Note: You do not need to solve for the exact probability; you just need to choose the equation below that correctly represents how you would solve for this probability.

c. P(X=7)= 10!/7!3! (0.81)^7(0.19)^3

The results for a blood test for a certain disease are shown in the table below. Let D represent disease status (whether or not the person actually has the disease) and T represents test results. Based on the table, what is the prevalence of the disease? In epidemiology, prevalence is the proportion of a particular population found to be affected by a medical condition. a. 0.09 b. 0.97 c. 0.0725 d. 0.075 e. 290

d. 0.075

Use the following information for questions 4-6: Cholesterol levels for women ages 20-34 are approximately normally distributed with a mean of 185 mg/dL and a standard deviation of 39 mg/dL. Cholesterol levels above 240 mg/dL are considered high. What is the probability that a woman between the ages of 20 and 34 has a high cholesterol level (that is, her cholesterol is above 240 mg/dL)? a. 1.41 b. 0.0808 c. 0.9192 d. 0.0793 e. 0.1586 f. 0.9207

d. 0.0793

Suppose heights of adult American women are normally distributed with a mean of 65 inches and a standard deviation of 3.5 inches. Michelle Obama is a 57 year old American woman. Her doctor tells her that her height is above average but less than 2 standard deviations away from the mean. Which of the following could potentially be the z-score of her height? a. -0.73 b. More than one of the above c. Impossible to Determine d. 1.50 e. 2.00

d. 1.50

Suppose you have a data set with the following five number summary: Minimum = 26, Q1 = 32, Median = 34, Q3 = 38, Maximum = 58. What is the lower cutoff point for potential outliers? (By lower cutoff point, we mean the number such that anything smaller than it is an outlier). a. 14 b. 47 c. 29 d. 23 e. 56

d. 23

Jim is conducting a health survey of residents of Brazos County. He asks them their age, gender, height, weight, type of insurance, marital status, income, and number of days they were sick in the last month. The possible values for marital status are married, widowed, divorced/separated, single/never married, and living with a partner but not married. How many of the variables in the health survey were categorical and how many were numeric? a. 5 categorical and 3 numeric b. 4 categorical and 4 numeric c. 2 categorical and 6 numeric d. 3 categorical and 5 numeric e. 6 categorical and 2 numeric

d. 3 categorical and 5 numeric

A researcher wants to determine if a new exercise program helps people lose weight. She recruits over 1200 subjects (her statistician determined this number from sample size calculations) and randomly assigns them to either participate in the new exercise program or no-exercise program. She personally interacts with the participants while assigning the treatments. She tells those in the new program group to exercise 3 times a week and tells those in the no-exercise group that they should not exercise for the duration of the study. Based on this information, which of the following principles of experimental design is not ensured in this study? a. Control/Placebo b. Sample Size c. Randomization d. Blinding

d. Blinding

Use the following information for questions 28-31: A researcher wants to determine if there is an association between gender (only male and female are considered for ease) and the political party they prefer to vote. She interviewed 1000 random individuals and recorded their gender and their political party. The results are shown in the table below. Conduct the appropriate hypothesis test using a 0.05 significance level. What are the hypotheses? a. H0: Gender and voting preferences are related. HA: Gender and voting preferences are associated. b. H0: p1 = p2 HA: p1 < p2 c. H0: Gender and voting preferences are associated. HA: Gender and voting preferences are independent. d. H0: Gender and voting preferences are independent. HA: Gender and voting preferences are associated. e. H0: p1 = p2 HA: p1 > p2

d. H0: Gender and voting preferences are independent. HA: Gender and voting preferences are associated.

Consider the population of all students at your school. A certain proportion support removing vending machines. Your friend randomly samples 20 students from the​ school, and uses the sample proportion who support removing vending machines to predict the population proportion at the school. You take your​ own, separate random sample of 20 ​students, and find the sample proportion that supports removing vending machines. How likely is it that the sample proportions are the​ same? a. It is very unlikely that the sample proportions will be the same because the samples come from different populations. b. It is impossible that the sample proportions will be the same because the samples are different. c. It is likely that the sample proportions will be the same because the sample sizes are the same. d. It is unlikely that the sample proportions will be exactly the same.​ However, they should be close to each other because the samples represent the same population. e. It is likely that the sample proportions will be the same because the sample represents the same population.

d. It is unlikely that the sample proportions will be exactly the same.​ However, they should be close to each other because the samples represent the same population.

Bonus: A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) that she observed at her southern Florida home last year. The coldest temperature for any week was 36 degrees F but she mistakenly recorded the Celsius value of 2 degrees. Assuming that she correctly listed all the other temperatures, how will this error affect the mean and the median? a. It will cause both the mean and the median to decrease. b. Both the mean and the median will be unaffected. c. It will cause the median to decrease, but the mean will be unaffected. d. It will cause the mean to decrease, but the median will be unaffected.

d. It will cause the mean to decrease, but the median will be unaffected.

Use the following information for questions 28-31: A researcher wants to determine if there is an association between gender (only male and female are considered for ease) and the political party they prefer to vote. She interviewed 1000 random individuals and recorded their gender and their political party. The results are shown in the table below. Conduct the appropriate hypothesis test using a 0.05 significance level. The chi-square test statistic for this test is 16.2037. What is the p-value? Use the following information for questions 28-31: A researcher wants to determine if there is an association between gender (only male and female are considered for ease) and the political party they prefer to vote. She interviewed 1000 random individuals and recorded their gender and their political party. The results are shown in the table below. Conduct the appropriate hypothesis test using a 0.05 significance level. The chi-square test statistic for this test is 16.2037. What is the p-value? a. 0.01 < p-value < 0.02 b. p-value > 0.001 c. p-value = 1 d. p-value < 0.001 e. p-value = 0.001

d. p-value < 0.001

Tom Brady wants to know what proportion of his fans watched the Super Bowl on Feb 7, 2021. He takes a simple random sample of 500 fans and asks them. All of the randomly chosen 500 fans respond to this survey, and 495 (99%) of them respond that they watched it. What is the statistic and what is its value? a. The statistic is the group of the Tom Brady fans who were sampled, which is 500. b. The statistic is the proportion of all Tom Brady fans who watched the Super Bowl, which is unknown. c. The statistic is the average number of all Tom Brady fans who watched the Super Bowl, which is 495. d. The statistic is the proportion of the sampled Tom Brady fans who watched the Super Bowl, which is 0.99. e. The statistic is the proportion of all Tom Brady fans who watched the Super Bowl, which is 0.99. f. The statistic is the proportion of the sampled Tom Brady fans who watched the Super Bowl, which is unknown.

d. The statistic is the proportion of the sampled Tom Brady fans who watched the Super Bowl, which is 0.99.

Below is a histogram of the IQ ("intelligence quotient") scores of 60 fifth-grade students chosen at random from a school. The range is defined as the maximum minus the minimum. What is the range of this distribution? a. 70 b. 150 c. 79 d. 80 e. 75

d. 80

Eli wants to determine whether or not there is an association between gender and GPA among high school seniors in Ohio. He randomly selects 200 high school seniors at Amelia High School, a public school in southwest Ohio. He asks them to report their gender, as well as their current GPA. Out of these 200 students, 117 were female and 83 were male. The average GPA of the 117 female high school seniors was 3.6. What is the population of interest in this study? a. The 200 students randomly selected to take in the survey b. All high school seniors at Amelia High School c. All high school students d. All high school seniors in Ohio e. All high school seniors

d. All high school seniors in Ohio

Your local school board wants to determine if the proportion of people who plan on voting for the school levy in the upcoming election is different for families who have elementary aged students and families that do not. They conduct a random phone poll, where they contact 200 families. Of the 100 families with elementary aged students, 75 say they plan on voting for the levy. Of the 100 families without elementary aged students, 68 say they plan on voting for the levy. Let Group A = Families with Elementary Aged Students and Group B = Families without Elementary Aged Students. Assume all conditions are met. Create a 98% confidence interval for the difference between the two proportions. a. (-0.055, 0.195) b. (0.078, 0.218) c. 2.326 d. (-0.218, 0.078) e. (-0.078, 0.218) f. (-0.0042, 0.1442)

e. (-0.078, 0.218)

Given the probabilities shown below, what is P(A⋂B)? P(A) = 0.65 P(B) = 0.32 P(B|A) = 0.75 a. 0.220 b. Impossible to Determine c. 0.240 d. 0.208 e. 0.4875

e. 0.4875

Use the following information for questions 4-6: Cholesterol levels for women ages 20-34 are approximately normally distributed with a mean of 185 mg/dL and a standard deviation of 39 mg/dL. Suppose a researcher wants to determine the cholesterol level such that 85% of all women between the ages of 20 and 34 have cholesterol levels higher than that. What is the cholesterol level? a. 225.56 mg/dL b. Impossible to determine c. 225.17 mg/dL d. 144.83 mg/dL e. 144.44 mg/dL f. -1.04 mg/dL

e. 144.44 mg/dL

The boxplot below shows the distribution of heights of 16 undergraduate statistics students. Using this boxplot, approximately how many students are 69 inches or taller?The boxplot below shows the distribution of heights of 16 undergraduate statistics students. Using this boxplot, approximately how many students are 69 inches or taller? a. Impossible to Determine b. 12 c. 16 d. 8 e. 4

e. 4

Because of the increasing nuisance of spam email messages, many start-up companies have emerged to develop e-mail filters. One such filter was recently advertised as being 81% accurate. This could mean one of four things. One thing it could mean is that 81% of valid email is allowed through. Let S denote the event that the message is spam and let B denote the event that the filter blocks the message. Which of the following expresses the statement, "81% of valid email is allowed through," as a conditional probability? a. P(S|B) = 0.81 b. P(B|S) = 0.81 c. P(Bc|S) = 0.81 d. P(Sc|Bc) = 0.81 e. P(Bc|Sc) = 0.81

e. P(Bc|Sc) = 0.81

Use the following information for questions 26-27: Rock-paper-scissors is a game played by two or more people where players choose either rock, paper, or scissors with their hands. For your statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. The following table summarizes the data: What is the test statistic for the chi-square goodness of fit test? a. 0.0005 b. 0 c. 7.51 d. 0.20 e. 0.317 f. 0.30

f. 0.30

The IQs of elementary aged children are approximately normally distributed with a mean of 100 and a standard deviation of 15. Using the empirical rule, approximately what percent of elementary aged children have an IQ between 85 and 130? a. 47.5% b. 13.5% c. 81.85% d. 68% e. 95% f. 81.5%

f. 81.5%