STA Exam 3

A significance test is conducted to determine if the majority of students at UF have a paying job at some time during the year? Ho: p=0.5 vs Ha: p>0.5 What would a Type I Error mean in this setting? A. Determining that it is more than half of students in the population who have a job when in fact, it is really not. B. Determining that it is more than half of students in the population who have a job when that is the truth about the population. C. Determining that it is NOT more than half of students in the population who have a job when in fact, it really is more than half. D. Determining that it is NOT more than half of students in the population who have a job when in fact, it really is NOT more than half.

A

A scientist was interested in studying if students political beliefs change as they go through college. Two hundred randomly selected students were asked before they entered college if they would consider themselves liberal or conservative. Four years later, the same two hundred students were asked if they would consider themselves, liberal or conservative. The scientist decided to perform McNemar's test. The data is below. What is the test statistic? After College Before College Liberal Conservative Liberal 80 15 Conservative 20 85 A. 1.96 or -1.96 B. -0.85 or 0.85 C. -0.39 or 0.39 D. -9.75 or 9.75

B

A small county has two property appraisers, Tim and Julie. Does Tim appraise property differently on average than Julie? Each appraiser looks at 20 properties and each independently determines the value of the property (Tim - Julie) How should we write the alternative hypothesis? (mud is the population mean difference) A. Ha: mud < 0 B. Ha: mud does not equal zero C. Ha: mud = 0 D. Ha: mud > 0

B

An education specialist was studying SAT math scores at a local university. She found that the following 95% confidence interval for the population mean score for SAT math: (450, 550). Suppose that a significance test at Ho: population mean equals 345 versus Ha: population does not equal 345. The p-value for this test was 0.0007. Which of the following statements accurately describes the situation? A. The population mean score for SAT Math is practically (but not statistically) different from 345. B. The population mean score for SAT Math is statistically and practically different from 345. C. The population mean score for SAT Math is NOT statistically and practically different from 345. D. The population mean score for SAT Math is statistically (but not practically) different from 475.

B

Do less Republicans (group A) than Democrats (group B) favor the government investing billions of dollars to improve the country's train system? One thousand Republicans and one thousand Democrats were asked if they favored spending billions to improve the country's train system. How would we write the alternative hypothesis? A. Ha: pA-pB=0 B. Ha: pA-pB < 0 C. Ha: pA-pB > 0 D. Ha: pA-pB does not equal 0

B

In Spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many hours they had worked the previous day. The 95% confidence interval comparing underclassmen to upperclassmen was (-0.233, 1.1250) Interpret the interval. "We are 95% confident that the __________________ hours of work for underclassmen is between 0.233 __________ to 1.125 __________ that upperclassmen." A. Sample Mean, More, Less B. Population Mean, Less, More C. Population Mean, More, Less D. Sample Mean, Less, More

B

Should we focus on the p-value instead of the alpha level? A. No-there is no relationship between alpha and the p-value B. Yes-alpha is arbitrary, while the p-value gives a better representation of the amount of evidence we have to reject the null C. No answer text provided D. Doesn't matter-alpha and the p-values are the same thing

B

Do people improve their timing on an online crossword puzzle with an additional attempt? Twenty people were timed to complete a crossword puzzle online. After a twenty minute break, they were asked to complete the crossword puzzle online again. Was there an improvement in their time? (first-second) The p-value was 0.06. Interpret. With a p-value of 0.06, we have _______ statistically significant evidence that the _____________ time to complete the puzzle has improved. A. strong B. some C. no D. population mean E. sample mean

B & D

Which of the following are assumptions for the confidence interval for the different between two population means? A. There are at least 15 successes and 15 failures B. Random Samples C. Data is Quantitative D. Data is Categorical E. Data is from a Convenience Sample F. Both sample size are greater than 30 or the data from a Normal Distribution

B, C, & F

A social scientist is interested in determining if there is a significant difference in the proportion of Republicans between two areas of town. He takes independent random samples of 200 families in each area of town and a significance test was conducted. The p-value was 0.416. What should be our conclusions? A. The evidence is very strong-there is a difference in proportion of Republicans between the two areas of town. B. The evidence is pretty strong-there is a difference in proportion of Republicans between the two areas of town. C. We do not have statistical significant evidence to say that there is a significant difference in proportion of Republicans in two areas in town.

C

A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Has there been improvement? (pre-post) What value of t would you use for the 99% confidence interval? Student 1 2 3 4 5 Pre-Test 12 14 11 12 13 Post-Test 15 17 15 20 13 A. 2.776 B. 2.576 C. 4.604 D. 2.571 E. 4.032

C

An agricultural field test compares two varieties of corn, silver queen and country gentlemen. The researchers take 10 plots and divide each of these plots in half. Each plot has a similar amount of sun light, shade, quality of soil and irrigation. The variety of corn is randomly chosen for each half of a plot. After the harvest, the yield of corn is measured for each half plot of each location. The yield from silver queen was compared to the yield of country gentlemen. Note: Differences were taken by taking Variety A - Variety B. The 95% confidence interval for the mean is (-0.223, 0.988). What is the correct interpretation of this interval? A. We have sufficient evidence to show that variety B has a higher population mean yield than variety A, at 95% confidence. B. There is convincing evidence that variety A has a higher population mean yield than variety B, at 95% confidence. C. There is convincing evidence that population mean yield of variety A is different from variety B, at 95% confidence. D. There is not enough evidence to say that variety A has a different mean yield then variety B, at 95% confidence.

C

Do students that are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student government events than students who are "Not Greek"? Specifically, do more "Greek" students than "Not Greek" vote in the student elections? Let "Greek" students be group A and "Not-Greek" students be group B. Out of 250 randomly selected "Greek" students, 200 voted in the last election. Out of 500 randomly selected "Not Greek" students, 140 randomly selected "Not Greek" students voted in the last election. How would we write the alternative hypothesis? A. Ha: pA-pB=0 B. Ha: pA-pB < 0 C. Ha: pA-pB > 0 D. Ha: pA-pB does not equal 0

C

In Spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many concerts they had attended in the past six months For the 39 randomly selected upperclassmen, the sample mean was 2.31 and sample standard deviation was 2.32. For the 35 randomly selected underclassmen, the sample mean was 2.29 and the sample standard deviation was 2.64. What is the point estimate of the difference in the population mean difference in number of concerts attended between underclassmen and upperclassmen? A. Unknown B. 0 C. 0.02 D. -0.32

C

In Spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many hours they had volunteered in the past 24 hours. For the 39 randomly selected upperclassmen, the sample mean was 0.12 and sample standard deviation was 0.42. For the 35 randomly selected underclassmen, the sample mean was 0.34 and the sample standard deviation was 0.87. What is the point estimate of the difference in the population mean volunteered between underclassmen and upperclassmen? A. Unknown B. 0 C. -0.22 D. -0.45 E. 4

C

Many non-profit groups ask for donations during December. Do men give higher monetary donations than women in the month of December? How should we write the alternative hypothesis? Let mum be the population mean donation for men and let muw be the population mean donation for women. A. Ha: mum-muw does not equal 0 B. Ha: mum-muw < 0 C. Ha: mum-muw > 0 D. Ha: mum-muw = 0

C

On average, do women spend more on haircuts than men? Someone took a random sample of men and women at UF and asked them how much they had spent on their last hair cut. A portion of the Minitab output appears below. What is the best interpretation of the output below? Difference= mu(F) - mu(M) T-Test of difference= 0(vs >): T-Value= 3.82 P-Value= 0.000 DF= 68 A. With a p-value equal to 0.000, there is statistically significant evidence of a difference in average amount of money spent on hair cuts between men and women at UF. B. With a p-value equal to 0.000, there is statistically significant evidence that the average amount of money spent on hair cuts for men is higher than it is for women at UF. C.With a p-value equal to 0.000, there is statistically significant evidence of that the average amount of money spent on hair cuts for women is higher than it is for men at UF. D. With a p-value equal to 0.000, there is no statistically significant evidence of a difference in average amount of money spent on hair cuts between men and women at UF.

C

What is the definition of Type 2 error? A. Failing to reject the null hypothesis when the null hypothesis is really true. B. Rejecting the null hypothesis when the null hypothesis is really true. C. Failing to Reject the null hypothesis when the null hypothesis is really false. D. Rejecting the null hypothesis when the null hypothesis is really false.

C

When we make inferences about the difference of two independent population proportions, what assumptions do we need to make? A. Sample size must be greater than or equal to 30. B. The sum of the counts of successes and failures must be greater than 30. C. Counts of successes and failures at least 15 each for each group. D. Normal distribution of the response variable. E. Random samples.

C & E

A major grocery store chain is trying to cut down on waste. Currently, they get peaches from two different distributors, Whole Fruits and Green Grocer. Out of a two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. She then makes a confidence interval. Is there a significant difference in the quality of the peaches between the two distributors? 95% CI for pW-pG: (0.064, 0.156) A. We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 LOWER and 0.156 HIGHER than the proportion of non sell-able items for Green Grocer. B. We are 95% confident that the proportion of non sell-able peaches from Green Grocer is anywhere between 0.064 and 0.156. C. We are 95% confident that the proportion of non sell-able peaches from Whole Fruits is anywhere between 0.064 and 0.156 D. We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156 HIGHER than the proportion of non sell-able items for Green Grocer. E. We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156 LOWER than the proportion of non sell-able items for Green Grocer.

D

A scientist was interested in studying if students beliefs about binge drinking change as they go through college. Forty randomly selected students were asked before they entered college if they thought that binge drinking was wrong or ok. Four years later, the same forty students were asked if thought that binge drinking was wrong or ok. The scientist decided to perform McNemar's test. The data is below. Are the assumptions met? After College Before College OK Wrong O.K 15 8 Wrong 5 12 A. No, n is not greater than 30 B. Yes, n is greater than 15 C. Yes, n is greater than 30 D. No, YN + NY is not greater than or equal to 30 E. Yes, YN + NY is greater than or equal to 30

D

A teacher wants to see if a new unit on fractions is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Suppose that you are about to compute a confidence interval for ud, how do you check for normality? A. You don't have to check for normality for this type of data. B. Make a plot of the pre and post test scores and see if there are any outliers. C. You don't have to check for normality since the values are large enough. D. Find the difference between the two scores for each subject. Make a plot of the differences and check for outliers.

D

In 2012, the General Social Survey included a question that asked respondents if they had "often/sometimes" been the subject of gossip at work. Out of 606 men, 75 said yes they had "often/sometimes" been the subject of gossip at work. Out of 580 women, 67 said yes they had "often/sometimes" been the subject of gossip at work. What is the pooled proportion for the null hypothesis Ho:p1-p2=0 vs. alternative hypothesis Ha: p1-p2 does not equal 0? A. 0.124 B. 0.116 C. 0.662 D. 0.120 E. Unknown

D

In 2012, the General Social Survey included a question that asked respondents if they had "often/sometimes" been ignored at work. Out of 613 men, 78 said yes they had "often/sometimes" been ignored at work. Out of 588 women, 90 said yes they had "often/sometimes" been ignored at work. What is the pooled proportion for the null hypothesis Ho: p1-p2=0 vs. alternative hypothesis Ha: p1-p2 does not equal 0? A. 0.1977 B. 0.901 C. Unknown D. 0.1442 E. 0.140

E

A scientist was interested in studying if students beliefs about illegal drug use change as they go through college. A scientist randomly selected 104 students and asked them before they entered college if they thought that illegal drug use was wrong or ok. Four years later, the same 104 students were asked if thought that illegal drug use was wrong or ok. The scientist decided to perfom McNemar's test. The data is below. What is the proportion of students that thought is was wrong before college? After college After college (four years later) (four years later) OK Wrong Before college OK 4 17 Before college wrong 18 65 A. 0.17 B. 0.82 C. 0.18 D. 0.65 E. 0.04 F. 0.80

F