ST 311

A police officer wants to know the proportion of crimes that are burglaries within the last five years. She randomly selects 40 records from a database of all crimes and checks their records. She finds that 30% of the crimes were labeled as burglary within the last five years. Select one: a. Yes. b. No, because it wasn't a random sample. c. No, because n(p-hat) < 10 or n(q-hat) < 10. d. No, because the sample size wasn't at least 30 and the population wasn't normally distributed. e. No, because we already know the population proportion.

a

In January 2019, the American Midwest experienced record-breaking freezing temperatures. A certain metropolitan area in Wisconsin, with a residential population of over 1.5 million, experienced daily average temperatures as low as minus 20 degrees Fahrenheit. Hospitals saw a steady stream of patients reporting symptoms of frostbite. In the aftermath, a survey was conducted in order to estimate the true proportions of individuals afflicted by frostbite during the extreme weather. 350 residents were selected via simple random sampling and 336 reported not having any symptoms. What was the sample proportion obtained by the survey? Give your answer to 3 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response." (Note it's the sample proportion of people who did have frostbite.)

350 - 336 = 14 sample proportion = 14/350 = 0.040

A researcher was interested in utilities provided by city governments. The researcher randomly selected 20 counties from a list of all counties in the U.S. From each of these counties the researcher then contacted each city government (a total of 192) and found that 12 (6.25%) of them provided electricity to their residents. The type of sample used in this example is a

cluster random sample.

Our friend the waffle-man is back and wants to do more hypothesis tests for proportions, but this time for four waffle recipes. He randomly selected 250 waffle consumers and found that 100 (40%) of the 250 preferred Waffle No. 2. He conducted a hypothesis test with H0:p=0.25H0:p=0.25, Ha:p>0.25Ha:p>0.25. Notice the proportion under the null distribution is p_0 = 0.25. The test statistic for this problem is 5.47. You can verify for yourself that the probability of observing this test statistic is nearly zero assuming the null hypothesis is true. Now suppose we wish to conduct the same hypothesis test again if the true proportion is 0.35. In other words, we happen to know the true parameter value is 0.35, something that is typically not known. How does the test statistic change with this new information? What is the resulting p-value? Hint: Try writing what the null hypothesis and test statistic would be given this new information. What would change, if anything? Select one: a. The test statistic becomes 1.61 with a p-value of 0.537. b. The test statistic becomes 1.66 with a p-value of 0.095. c. The test statistic becomes -3.23 with a p-value of 0.9995. d. The test statistic does not change from its original value of 5.47, and the associated p-value does not change. e. None of the other answers are correct.

d

Which of the following scenarios involving proportions would be appropriate for conducting inference? Select all that apply. Select one or more: a. A researcher wishes to find the probability that more than 75% of a sample of undergraduate students from Winston Salem State University will be female. He randomly samples 30 undergraduate students from the student database. The population proportion of undergraduate females at WSSU is known to be 70.7%. b. A researcher wishes to find the probability that more than 16% of a sample of undergraduate students from UNC Charlotte will be between the ages of 25 and 34. He samples the first 75 students that walk into the gym on Monday morning. The population proportion of undergraduates between the ages of 25 and 34 is known to be 14.4%. c. A grad student at UNC wants to know how likely it is that a group of students would be made up of less than 35% graduate students. She will ask 25 of her UNC friends if they are a graduate student or an undergraduate student. The population proportion of grad students and UNC is 36.8%. d. A full time student at Appalachian State University wants to know how likely it is that a group of students would be made up of more than 90% full time students. She will randomly ask 85 students their enrollment status. The population proportion of full time students at Appalachian State is 88%

d

An electronic device factory is studying the length of life of the electronic components they produce. The manager takes a random sample of 50 electronic components from the assembly line and records the length of life in the life test. From the sample he found the average length of life was 100,000 hours and that the standard deviation was 3,000 hours. He wants to find the confidence interval for the average length of life of the electronic components they produced. Based on the information, what advice would you give to him? Select one or more: a. The distribution of the length of life of the electronic components is usually right skewed. Thus, he should not compute the confidence interval. b. He did not take a simple random sample of the electronic components; thus he should not compute the confidence interval c. The mean and standard deviation are large enough to compute the confidence interval. d. The sample size is large enough to use a normal approximation. Thus he can compute the confidence interval. e. He can calculate the confidence interval but should use a t-distribution because the population standard deviation is unknown.

d,e

We are conducting a test of the hypotheses H0: p = 0.28 Ha: p ≠ 0.28 We find a test statistic of z = -1.45. What is the corresponding p-value? Give your answer as a proportion between 0 and 1 to 4 decimal places.

p = 0.0735*2 = 0.1470

Polling suggests that 45% of the US adult population does not own a car. A random sample of 500 Americans will be taken. The sampling distribution of a sample proportion suggests that: (select all of the following which are correct) Select one or more: a. 45% of the 500 Americans sampled will not own a car. b. Since the 500 Americans are randomly sampled, we cannot make any kind of predictions about the resulting sample proportion. c. It is less likely for less than 40% of the 500 Americans sampled to not own a car than it is for more than 50% of the Americans sampled to not own a car. d. It is more likely for less than 46% of the 500 Americans sampled to not own a car than it is for more than 45% of the Americans sampled to not own a car. e. Across a large number of random samples, we should expect that, on average, 45% of the 500 Americans sampled will not own a car.

sigma = sqrt(0.45*0.56)/500 = 0.02245 Empirical Rule: Upper bound - 0.45 + 3*0.02245 = 0.52 Lower bound - 0.45 - 3*0.02245 = 0.38 d. - 0.46 - 0.38 = 0.08 0.52 - 0.46 = 0.06 d,e

At a large university it is known that 40% of the students live on campus. The director of student life is going to take a random sample of 200 students. Which of the following is most likely to occur. Select one: a. The sample proportion falls between 0.4 and 0.6 b. The sample proportion falls between 0.2 and 0.4 c. The sample proportion falls between 0.3 and 0.5 d. The sample proportion falls between 0.35 and 0.45

sigma of sample proportion = sqrt(0.4*0.6)/sqrt200 = 0.034641 Empirical rule: Upper bound - 0.4 + 3*0.034641 = 0.5039 Lower bound - 0.4 - 3*0.034641 = 0.296077 c

An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made the exam harder than he had intended. The scores were very symmetric, but the average score for his students was 43 and the standard deviation of the scores was 5 points. The instructor is considering 2 different strategies for rescaling the exam results: Method 1:Add 17 points to everyone's score. Method 2:Multiply everyone's score by 1.7. Which of the following are true? Select all that apply. A. Method 2 will increase the standard deviation of the students' scores. B. Method 1 will increase the standard deviation of the students' scores. C. Method 2 will decrease the standard deviation of the students' scores. D. Method 1 will decrease the standard deviation of the students' scores.

A

In engineering and product design, it is important to consider the weights of people so that airplanes or elevators aren't overloaded. Based on data from the National Health Survey, we can assume the weight of adult males in the US has a mean weight of 197 pounds and standard deviation of 32 pounds. We randomly select 64 adult males. What is the probability that the average weight of these 64 adult males is over 192 pounds? Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Check Assumption: Radom sample, n >= 30 Sigma of sample mean = 32/sqrt64 = 4 z = (192 - 197)/4 = -1.25 P (z > -1.25) = 1 - 0.1056 = 0.8944

A sample of 1000 college students at NC State University were randomly selected for a survey. Among the survey participants, 102 students suggested that classes begin at 8 AM instead of 8:30 AM. The sample proportion is 0.102. What is the upper endpoint for the 99% confidence interval? Give your answer to three decimal places. (Note that due to the randomization of the questions, the numbers in this question might be different from the previous question.)

Check Assumption Z* = 2.58 Margin of Error = 2.58 * Sqrt (0.102 * 0.898)/Sqrt 1000 = 0.025 Upper bound = 0.102 + 0.025 = 0.127

A sample of 1000 college students at NC State University were randomly selected for a survey. Among the survey participants, 108 students suggested that classes begin at 8 AM instead of 8:30 AM. The sample proportion is 0.108. What is the margin of error for a 90% confidence interval for this sample? Give your answer to three decimal places.

Check Assumption: Random Sample, np-hat = 108 nq-hat = 892 Z* = 1.64 Margin of error = 1.64 * Sqrt(0.108*0.892)/Sqrt1000 = 0.016

In psychology, there is a particular Mental Development Index (MDI) used in the study of infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. We are going to randomly select 64 children and average their MDI scores. What is the probability that the average is under 97? Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Check Assumption: random sample n >= 30 Sigma of sample mean = 16/sqrt64 = 2 z = (97 - 100)/2 = -1.5 p (z < -1.5) = 0.0668

At North Carolina State University it is known that 44% of undergraduates are female. If a random sample of 100 undergraduate students was taken, which of the following would accurately describe the sampling distribution?Select all that apply. Select one or more: a. The sampling distribution will be approximately normal. b. The sampling distribution will be skewed right. c. The sampling distribution will be skewed left. d. The mean of the sampling distribution will be close to 50% e. The mean of the sampling distribution will be close to 44% f. We can not determine the mean of the sampling distribution from the given information. g. The standard deviation of the sampling distribution will be 0.0496 h. The standard deviation of the sampling distribution will be 0.0025. i. The standard deviation of the sampling distribution will be 0.4964. j. We can not determine the standard deviation of the sampling distribution from the given information.

Check Assumption: random sample np = 100*0.44 = 44 nq = 100*0.56 = 56 Sigma = sqrt(0.44*0.56)/sqrt100 = 0.049639 a,e,g

At a large university it is known that 51% of the students live on campus. The director of student life is going to take a random sample of 100 students. What is the probability that more than half of the sampled students live on campus?

Check Assumption: random sample np = 51 nq = 49 Sigma of sample mean = sqrt(0.51*0.49)/sqrt100 = 0.04999 z = (0.50 - 0.51)/0.04999 = -0.20 p (z > -0.02) = 1-0.4207 = 0.5793

A statistics graduate student conducted an experiment about graduate students who lived on campus. After taking a simple random sample of 38 students, she found that ten students lived on campus. What is the standard error she calculated? Give your answer to 3 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Check Assumption: random sample np-hat = 10 nq-hat = 28 Standard erro = sqrt (0.26*0.74)/sqrt 38 = 0.071

The daily revenues of a cafe near the university are approximately normally distributed. The owner recently collected a random sample of 30 daily revenues and found a 95% confidence interval for the average daily revenues in his shop is (966.738, 1033.262). He is unsatisfied by the precision of this confidence interval, however, and wishes to reduce the margin of error by a factor of 3, while retaining the same level of confidence. What sample size do you suggest he use to obtain the desired margin of error? Assume the sample standard deviation remains the same as the sample size changes. Select one: a. 10 b. 90 c. 270 d. 900

MOE = t*s/sqrt n Reduce by 3, n need to be increased by 3-square. n*9 = 270

For each of the following, tell whether the population parameter of interest is µ or p. In a survey, 36 males from NC State were asked their weight. Their average weight was 195.8 lbs with a standard deviation of 30.3 lbs. What is the average weight of males attending NC State? Answer 1 Choose...µp From a poll of 2,419 people who downloaded music illegally from the internet, only 2 reported that they were pirates. What proportion of people who download music illegally self-report as pirates? Answer 2 Choose...µp A recent study of 411 high-school students found that the average daily time they spent on cell phones was 100 minutes. What is the average daily time spent on cell phones among all students at the high school? Answer 3 Choose...µp

Quantitative - µ Categorical - p a. µ b. p c. µ

For the SAT college entrance exam (prior to March 2005), the combined scores ranged from 400 to 1600.A study recorded the combined scores from 100 students from each of three schools in a western state.The resulting scores were used to produce these box plots.

School 3 is more skewed right than school 1. The third quartile of school 2 is greater than 1400. The outliers for school 3 have a greater influence on the mean than the median.

From the records of a health-insurance companies in Pennsylvania, it is known that 80% of the accounts include dental coverage. A researcher would like to take a random sample of 500 accounts to review. Find the standard deviation of the sample proportion in this situation. Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Sigma of sample proportion = Sqrt(0.8*0.2)/Sqrt500 = 0.0179

The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plans on showcasing a simple random sample of its dogs in a show. Depending on which dogs are chosen, the proportion of emotional support trained dogs may vary. In a sample of 50 dogs, what is the probability that less than 6% of the dogs are emotional support trained? Give your answer to four decimal places.

Sigma of sample proportion = sqrt(0.23*0.77)/sqrt50 = 0.059515 Z = (6%-23%)/0.059515 = -2.86 P (z<-2.86) = 0.0021

Alice knows that 70% of the creatures in Wonderland are anthropomorphic animals. She randomly invites several of Wonderland's inhabitants to a tea party. Depending on which inhabitants of Wonderland are chosen, the proportion of animals invited may vary. If Alice samples 60 inhabitants, what is the probability that more than 65% of the sampled inhabitants are animals? Give your answer to four decimal places.

Sigma of sampling proportion = sqrt(0.7*0.3)/sqrt60 = 0.059161 Z = (65%-70%)/0.059161 = -0.85 P (z>-0.85) = 1 - 0.1977 = 0.8023

John is a new college graduate working at his first job. After years of living in an apartment he has decided to purchase a home. He has found a great neighborhood from which he can walk to work. Before buying a home in the area he has decided to collect some data on the homes in this neighborhood. A data set has been compiled that represents a sample of 100 homes in the neighborhood he is considering. The variables included in this data set include:* Value: the current value of the home as determined by the county tax assessor.* Size: the size of the home in square feet.* Year: the year the homes were built.* Basement: does the home have a basement (y=yes, n=no).* Fireplace: does the home have a fireplace (y=yes, n=no).* Type: the structure a single family house or a townhouse. (house or townhouse).

The histogram for value is clearly bimodal. The reason it is bimodal appears to be because the neighborhood was built in two phases, the newer phase consists of larger more expensive homes and the older phase consists of smaller less expensive homes.

An instructor of a large college class gave an exam that has a possible total of 100 points. The instructor records the scores of 100 students from his class and produced the following histogram. The instructor says any score above a 90 is an A. Scores in the 80 to 89 range would be a B, scores between 70 and 79 would yield a C and below 70 would result in a failing grade.

The median grade is greater than the mean grade. The median grade is a A.

A researcher was interested in utilities provided by city governments. The researcher randomly selected 20 counties from a list of all counties in the U.S. From each of these counties the researcher then contacted each city in those counties (a total of 192) and found that 12 (6.25%) of them provided electricity to their residents.

The population of interest is all city governments in the U.S. The parameter of interest is the proportion of the city governments in the U.S. that provide electricity to their residents.

A professor wanted to determine the proportion of students in his class who have cheated on an exam. The professor selects a random sample of 30 students from his class and emails them the question "Have you ever cheated on an exam?". He receives responses from 10 of the 30 students. Which of the following statements are true?

This study suffers from non-response bias because only 33% of the people surveyed provided a response. This study suffers from response bias since students will not want to tell a professor whether or not they have cheated.

A researcher believes that the ankle circumference for adult females in Europe can be considered to have a normal distribution with a mean of 19 cm.If his belief is correct which of the following ranges of ankle sizes will have the largest proportion of members of this population? Select one: a. 10 to 16 cm b. 16 to 22 cm c. 22 to 28 cm d. It is impossible to tell without the standard deviation.

Within 3 times of standard deviation b

An insurance company wants to know the proportion of clients who have had claims within the last year. They randomly select 1000 clients from a database of all clients and checks their basic information. They find that 5% of the clients had claims within the last year.'Can we create a confidence interval for the relevant parameter? Select one: a. Yes. b. No, because it wasn't a random sample. c. No, because n(p-hat) < 10 or n(q-hat) < 10. d. No, because the sample size wasn't at least 30 and the population wasn't normally distributed. e. No, because we already know the population proportion

a

What is a sampling distribution? Select one: a. It is a probability distribution that quantifies which sample statistics are more and less likely to be observed. b. It is a probability distribution that quantifies which populations are more and less likely to have been sampled from. c. It is the true, unknown probability distribution of all parameters in the population. d. It is the true, average sample proportion across all possible sample proportions.

a

Which of the following scenarios would give a normal distribution? Select all that apply. Select one or more: a. The weights of 60 randomly selected highschool females were recorded. The minimum was 98 pounds and the maximum was 174 pounds. Most of the students weight between 130 and 140 pounds. b. 135 college students were asked how many hours a week they worked out. Most students reported working out fewer than 5 hours a week, but there were some students that reported working out as many as 20 hours per week. c. A large class took a difficult exam where the high score was a 72 and the low score was a 15. The average score was 24. d. All of the numbers ever drawn for the North Carolina Powerball were recorded and analyzed. No numbers appeared to be drawn more often than others.

a

A successful waffle-man has recently developed a new recipe for waffles. To test the popularity of this new waffle compared to two other tried-and-true types of waffles, our friend the waffle-man randomly selected 180 lucky customers to vote on which of the three waffle types they liked best. Exactly 35% of these customers (or 63 in total) voted in favor of the new waffle. If all waffles were equally tasty, then the waffle-man knows to expect that each waffle would receive around 1/3 of the votes (so around 60 votes per waffle). Are 63 votes for the new waffle enough to conclude that significantly more customers like it compared to the others? Luckily, our friend the waffle-man triple-majored in waffles, statistics, and clinical neurophysiology and knows how to objectively answer this question. He conducts a hypothesis test for proportions, H0:p=1/3H0:p=1/3, Ha:p>1/3Ha:p>1/3 with a sample proportion of 63/180. In carrying out this test, what null distribution for p̂ p^ should he use? In other words, what is the distribution of the sample statistic assuming the null hypothesis is true? (Be sure to use at least four decimal places in your calculations.) A normal distribution centered at 1/3 with a standard deviation of about 0.0351. b. A normal distribution centered at 1/3 with standard deviation of about 0.0356 c. A normal distribution centered at 0.35 with standard deviation of about 0.0356. d. A normal distribution centered at 0.35 with standard deviation of about 0.0351. e. We cannot use a null distribution in this problem because the population is not normally distributed.

a standard error = sqrt (0.33*0.67/180) = 0.351

According to the most recent census, the average total yearly expenses of households in Wake County is $38,500. It is also known that the distribution of household expenses in Wake County is strongly skewed to the right with a standard deviation of $10,500. A researcher is going to randomly select a sample of 5 households from Wake County. Which of the following is true? Select all that apply. Select one or more: a. The sampling distribution of the sample mean will have a smaller standard deviation than the population. b. The sampling distribution of the sample mean will have a different standard deviation than the population. c. The sampling distribution of the sample mean will be skewed right. d. The sampling distribution of the sample mean will have a larger standard deviation than the population. e. We cannot tell what the shape of the sampling distribution of the sample mean will look like. f. The shape of the sampling distribution of the sample mean will be approximately symmetric.

a,b,c

Which of the following are true? Select one or more: a. The t-distribution is dependent on the sample size. b. The t-distribution does not depend on the sample size. c. The t-distribution has more values at the extremes than a standard normal distribution. d. The t-distribution has fewer values at the extremes than a standard normal distribution. e. The t-distribution is bell-shaped and centered at its degrees of freedom. f. The t-distribution is bell-shaped and centered at 0. g. With larger samples, the t-distribution is closer to a normal distribution. h. With smaller samples, the t-distribution is closer to a normal distribution.

a,c,f,g

After taking an aptitude test, the computer told Bob that he had a z-score of -1.08.If scores on the aptitude test are normally distributed, which of the following statements can Bob conclude from his score? Select all that apply. Select one or more: a. Bob scored within 2 standard deviations of the mean score. b. Bob did better than the mean score. c. Bob scored within 1 standard deviation of the mean score. d. Bob did worse than the mean score. e. About 14% of students taking the aptitude test did better than Bob. f. About 14% of students taking the aptitude test did worse than Bob.

a,d,f

A sample of 108 college students at NC State University were randomly selected for a survey. The survey participants reported sleeping 6.8 hours a night on average with a sample standard deviation of 1.1 hours. Which of the following are true? Select one or more: a. The margin of error at 99% confidence is larger than that at 95% confidence. b. The margin of error at 99% confidence is smaller than that at 95% confidence. c. The margin of error is larger with a larger sample size. d. The margin of error is larger with a smaller sample size. e. The margin of error would be larger if the sample mean were 7.1 hours instead of 6.8 hours. f. The margin of error would be smaller if the sample mean were 7.1 hours instead of 6.8 hours. g. The margin of error would be larger if the sample standard deviation were larger. h. The margin of error would be larger if the sample standard deviation were smaller.

a,d,g MOE = t*s/sqrt n

In-N-Out Burger is planning on adding a new burger to the menu. A franchise owner wants to know how well the new burger would sell in Austin, Texas. As such, they want to estimate the proportion of residents in Austin, Texas that would like the new recipe. They randomly select 220 residents and have them taste the burger. Out of these 220 people, they determined that 143 of them enjoyed the burger. The sample proportion is 0.65, and the 95% confidence interval for the proportion of residents in Austin who like the new burger is: (0.587, 0.713). Assume where applicable that p-hat remains the same. a. If you created a 90% confidence interval instead of the 95% confidence interval the margin of error would? b. If you had a random sample of 98 residents instead of 220 the margin of error would? c. If you created a 99% confidence interval instead of the 95% confidence interval the margin of error would? d. If you had a random sample of 320 residents instead of 220 the margin of error would?

a. Decrease compared to confidence interval. b. Increase compared to confidence interval. c. Increase compared to confidence interval. d. Decrease compared to confidence interval.

A university officer wants to know the proportion of registered students that spend more than 20 minutes to get to school. He selects two parking decks at the university and talked with students at those decks. Of 25 students found in the decks, 12 have a commute under 20 minutes and 13 have a commute more than 20 minutes. Select one: a. Yes. b. No, because it wasn't a random sample. c. No, because n(p-hat) < 10 or n(q-hat) < 10. d. No, because the sample size wasn't at least 30 and the population wasn't normally distributed. e. No, because we already know the population proportion.

b

According to a recent report, it was found that 50.3% of residents in Cuyahoga county Ohio are registered to vote. Which of the following is more likely? Select one: a. We take a random sample of 10 people from this county and find that the proportion is over 55% b. We take a random sample of 200 people from this county and find that the proportion is over 55% c. We take a random sample of 500 people from this county and find that the proportion is over 55% d. We take a random sample of 1000 people from this county and find that the proportion is over 55% e. We have no basis for predicting which is more likely to have an proportion over 55%

b Apply to rule np >= 10, and nq >= 10

The city government has collected data on the square footage of houses within the city. They found that the average square footage of homes within the city limit is 1,240 square feet while the median square footage of homes within the city limits is 1,660 square feet. The city government also found that the standard deviation of home square footage within the city limits is 198 square feet. A statistician hired by a local home-carpeting company is going to randomly select a sample of 24 houses and record the square footage of the homes using public records. Which of the following is true? Select all that apply. Select one or more: a. The shape of the sampling distribution of the mean square footage of homes will be right skewed. b. The shape of the sampling distribution of the mean square footage of homes will be left skewed. c. If the statistician sampled 11 more homes within the city limits and added their data to the original sample of 24 homes then the shape of the sampling distribution of the mean square footage of all 35 homes will be approximately symmetric. Recall that the Central Limit Theorem says that if the sample size is greater than 30, then the sampling distribution of the mean will be symmetric. d. The sampling distribution of the mean square footage will have a smaller standard deviation when compared to the standard deviation of square footage among all homes within the city limits. e. The sampling distribution of the mean square footage will have a standard deviation equal to or larger than the standard deviation of square footage among all homes within the city limits.

b,c,d Recall that if the mean is larger than the median, the distribution is right skewed. If the mean is less than the median, the distribution is left skewed. And if the mean is equal to the median, or if the sample size is greater than 30, the distribution will be approximately symmetric.

Which of the following are true about the correlation coefficient r?Select all that apply. Select one or more: a. The correlation coefficient is always greater than 0. b. The correlation coefficient is always between -1 and +1. c. The correlation coefficient will change if we change the units of measure. d. If the correlation coefficient is positive, the slope of the regression line will also be positive. e. If the correlation coefficient is +1, then the slope of the regression line is also +1. f. If the correlation coefficient is close to 0, that means there is a strong linear relationship between the two variables.

b,d

A crop scientist is conducting research with a drought resistant corn hybrid. She is interested in determining if using fertilizer X will increase yield. She prepares 28 single acre plots and randomly assigns 14 to have normal soil while the other 14 are planted with fertilizer X. The resulting average yield for each group of 14 plots was recorded. Select one or more: a. The explanatory variable is the average yield for each group of 14 plots. b. The explanatory variable is whether the corn plants had fertilizer X or not. c. The response variable is whether the corn plants had fertilizer X or not. d. This is best described as an observational study. e. This study is best described as an experiment. f. The response variable is the average yield for each group of 14 plots.

b,e,f

About 480 women took part in a study about the effects of hormone therapy on middle-aged women; the women were grouped together in groups of two based on their similarities in height, weight, age, etc. Then one person in each group was randomly assigned to hormone therapy, while the other person was assigned to a placebo (they did not know which). After about a year, blood tests were conducted on each subject by a lab technician who was aware of which group (treatment or placebo) the blood samples originated from. In presenting the results of the experiment, the authors reported that the women in the treatment group had experienced a statistically significant increase in HDL (the so-called "good" cholesterol) and a statistically significant reduction in LDL (the so-called "bad" cholesterol) when compared with the control group. Select one or more: a. This study would be classified as double-blind. b. This study would be classified as single-blind. c. This study would be classified as un-blinded. d. The treatments were the HDL and LDL. e. The treatments were the hormone therapy and the placebo. f. The subjects are the 480 women in the study. g. The subjects are the blood tests. h. This is an example of a completely randomized design. i. This is an example of a matched pairs design.

b,e,f,i

A political action committee wanted to estimate the proportion of county residents who support the installation of red-light cameras throughout the county. They took a random sample of 900 county residents and found that the proportion who wanted to install these cameras was 24% with a margin of error of +/- 3% (with 95% confidence). This implies: Select one or more: a. There is a 95% chance that the true proportion of county residents who want the law changed is 24%. b. We believe that the true proportion of county residents who want the law changed is between 21% and 27%. c. We are 95% confident that the true proportion of county residents who want the law changed is between 21% and 27%. d. If we took another sample of 900 residents the sample proportion would definitely be between 21% and 27%. e. If we take many other samples of 900 residents from this population 95% of them will have a sample proportion that is between 21 and 27%. f. If we take 1000 other samples of 900 residents from this population, about 950 of them will produce confidence intervals that capture the true proportion. g. We cannot conclude anything about the population parameter since this is only a sample.

b. we believe that the true proportion of the county residents who want the law changed is between 21% and 27% c. we are 95% sure that the true proportion of the county residents who want the law changed is between 21% and 27%. g. we cannot conclude anything about the population parameter since this is only a sample.

A dessert manufacturer wanted to know if adding a preservative to their cupcakes extended their shelf life before going stale. They found the cupcakes that had the preservative lasted seven days before going stale, but the cupcakes without the preservative only lasted three days. They found that the difference in these shelf lives had a p-value of 0.24. Assume an αα of 0.05. What should we conclude about their findings? Select one: a. The results were statistically significant and practically significant. b. The results were statistically significant but not practically significant. c. The results were not statistically significant but were practically significant. d. The results were neither statistically significant nor practically significant.

c

A researcher has run an experiment and has properly calculated a confidence interval for a population mean parameter µ. Her 95% confidence interval is (0.351, 0.412). What is the probability that the true, unknown parameter µ is in her 95% confidence interval? Select one: a. 5% b. 95% c. Either 0% or 100%, but we don't know which. d. This isn't appropriate because confidence intervals are for sample statistics, not parameters. e. This isn't appropriate because confidence intervals are for population proportions, not population means.

c

The term statistical significance means Select one: a. the test statistic is close to what we would expect if the null hypothesis is true. b. the null hypothesis is true. c. the result we see is unlikely to happen just by random chance if the null hypothesis is true. d. the results are important and will make a practical difference in the lives of the subjects.

c

A farmer believes that his new irrigation method would result in more crop yield than the old one. To test his theory, he applies the new method to his corn fields. A total of 6 acres of sweet corn and 8 acres of flour corn are tested for the study. The farmer also thinks the method will work differently on sweet corn and flour corn. Therefore, he divides the group into sweet corn and flour corn and then randomizes the two methods within each group. The trainer measures the yield per acre, and then measures it again one year after the method has been implemented. Select one or more: a. The experimental units are the yield of corn. b. The treatments are the yield of corn. c. This is an example of a block design. d. The treatments are the new and old irrigation methods. e. The experimental units are the 6 acres of sweet corn and 8 acres of flour corn. f. This is an example of a matched pairs experiment. g. This is an example of a completely randomized experiment

c,d,e

A college professor stops at McDonald's every morning for 10 days to get a number 1 value meal costing $5.39. On the 11th day he orders a number 8 value meal costing $4.38.Which of the following are true?Select all that apply. Select one or more: a. During the first 10 days the professor's standard deviation was more than 0. b. During the first 10 days the professor's standard deviation was less than 0. c. During the first 10 days, the professor's standard deviation was 0. d. It is impossible to tell anything about the professor's standard deviation for the first 10 days. e. Considering all 11 days, the professor's standard deviation was lower than the standard deviation of the first 10 days. f. Considering all 11 days, the professor's standard deviation was higher than the standard deviation of the first 10 days. g. Considering all 11 days, the professor's standard deviation was the same as the standard deviation of the first 10 days. h. Considering all 11 days, It is impossible to tell anything about the professor's standard deviation compared to the first 10 days. Feedback

c,f

A clothing store owner wants to know the proportion of customers who used coupons within the last year. He selects in a random order all 2,000 receipts from a database of all purchases within the last year and finds that 340 of them are discounted by coupons. Select one: a. Yes. b. No, because it wasn't a random sample. c. No, because n(p-hat) < 10 or n(q-hat) < 10. d. No, because the sample size wasn't at least 30 and the population wasn't normally distributed. e. No, because we already know the population proportion.

e

Which of the following are true statements about the p-value?Select all that apply. Select one or more: a. The p-value is the probability the null hypothesis is correct. b. The p-value is the probability the alternative hypothesis is correct. c. The p-value is one minus the probability the alternative hypothesis is correct d. If the p-value is large it indicates we did not calculate the test statistic correctly. e. The p-value is calculated assuming the null hypothesis is true. f. The p-value is calculated assuming the alternative hypothesis is true. g. If the p-value is small it indicates the data is unlikely under the null hypothesis.

e,g

A psychologist has designed an index to measure the social perceptiveness of elementary school children. The index is based on ratings of a child's responses to questions about a set of photographs showing different social situations. A random sample of 16 elementary school children was chosen, and their index measurements were recorded. Assume that the index measure in the population is normally distributed. The 95% confidence interval created from this data is (56.29, 65.09). This interval indicates: Select one or more: a. The average index of elementary school children must be 60.69. b. The standard deviation of the sample is about 10% smaller than the population standard deviation. c. That if we take many samples from this population 95% of them will have a sample mean between 56.29 and 65.09. d. 95% of all elementary school children in this district have indices between 56.29 and 65.09. e. 4.40 is 95% of the true average of the index for all elementary school children. f. We are 95% confident that the average index for all elementary school children is between 56.29 and 65.09.

f

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 15. What proportion of children have MDI of at least 88? Select one: a .2119 b .7881 c .1056 d .8944

z = (88-100)/15 = -0.8 P (z>-0.8) = 1-0.2119 = 0.7881 b

For a normal distribution, what standard score (Z-score) has 20% of the distribution above it? Find the closest value listed on the table. Give your answer to 2 decimal places. For help on how to input a numeric answer, please see the Instructions.

z = 0.84

A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 531 and a standard deviation of 75. A local Junior High principal has decided to give an award to any student who scores in the top 10% of statewide scores.How high should a student score be to win this award? Give your answer to the nearest integer. For help on how to input a numeric answer, please see the instructions for entering numeric response.

z = 1.28 1.28 * 75 + 531 = 627