UMUC Stat200 quiz 3

STAT 200 Quiz 31. A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis?a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per dayb. Mean of hours that boys studied per day was greater than mean of hours that girls studied per dayc. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per dayd. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day2. A professor assumed there was a correlation between the amount of hours people were expose to sunlight and their blood vitamin D level. The null hypothesis was that the population correlation was__a. Positive 1. 0b. Negative 1. 0c. Zerod. Positive 0. 503. Conventionally, the null hypothesis is false if the probability value is: a. Greater than 0. 05b. Less than 0. 05c. Greater than 0. 95d. Less than 0. 954. A teacher hypothesized that in her class, grades of girls on a chemistry test were the same as grades of boys. If the probability value of her null hypothesis was 0. 56, it suggested: a. We failed to reject the null hypothesisb. Boys’ grades were higher than girls’ gradesc. Girls’ grades were higher than boys’ gradesd. The null hypothesis was rejected5. Which of the following could reduce the rate of Type I error?a. Making the significant level from 0. 01 to 0. 05b. Making the significant level from 0. 05 to 0. 01c. Increase the ? leveld. Increase the power6. ___is the probability of a Type II error, and ___ is the probability of correctly rejecting a false null hypothesis. a. 1-?, ?b. ?, 1-?c. ?, ?d. ?, ?7. A student hypothesized that girls in his class had the same blood pressure levels as boys. The probability value for his null hypothesis was 0. 15. So he concluded that the blood pressures of the girls were higher than boys’. Which kind of mistake did he make?a. Type I errorb. Type II errorc. Type I and Type II errord. He did not make any mistake8. When you conduct a hypothesis testing, at which of the following P-value, you feel more confident to reject the null hypothesis?a. 0. 05b. 0. 01c. 0. 95d. 0. 039. A student posed a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He found the P value of his null hypothesis was 0. 56. Thus, he could conclude: a. In September, Boston was colder than New Yorkb. In September, Boston was warmer than New Yorkc. He may reject the null hypothesisd. He failed to reject the null hypothesis10. If the P-value of a hypothesis test is 0. 40, you concludea. You accept the null hypothesisb. You reject the null hypothesisc. You failed to reject the null hypothesisd. You think there is a significant difference11. A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the test and the 95% confidence interval of grades was (83, 90). Can you reject the teacher’s assumption?a. Yesb. Noc. We cannot tell from the given information12. Which of the following descriptions of confidence interval is correct? (Select all that apply)a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0b. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1d. If a 95% confidence interval contains 1, then the 99% confidence interval contains 113. If a statistical test result is not significant at the 0. 05 level, then we can conclude: a. It is not significant at 0. 01 levelb. It is not significant at 0. 10 levelc. It must be significant at 0. 01 leveld. It must be significant above 0. 05 level14. Power is equal to: a. ?b. ?c. 1-?d. 1-?15. Which of the following descriptions of null hypothesis are correct? (Select all that apply)a. A null hypothesis is a hypothesis tested in significance testing. b. The parameter of a null hypothesis is commonly 0. c. The aim of all research is to prove the null hypothesis is trued. Researchers can reject the null hypothesis if the P-value is above 0. 0516. Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs. , 99 lbs, 101 lbs, 87 lbs, 140 lbs. What’s the sample standard deviation?17. Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs. , 99 lbs, 101 lbs, 87 lbs, 140 lbs. What’s the standard error of the mean?18. Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs. , 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the absolute value of calculated t that we use for testing the null hypothesis?19. Imagine a researcher posed a null hypothesis that in a certain community, the average energy expenditure should be 2,100 calories per day. He randomly sampled 100 people in that community. After he computed the t value by calculating a two-tailed t-statistic, he found that the probability value was 0. 10. Thus, he concluded: a. The average energy expenditure was bigger than 2,100 calories per dayb. The average energy expenditure was smaller than 2,100 calories per dayc. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per dayd. The average energy expenditure was either more than 2,100 calories per day or less than 2,100 calories per day20. Compared to the normal distribution, the t distribution has ___ values at the top and ___ at the tails. a. More, lessb. More, morec. Less, lessd. Less, more21. In order to test if there is a difference between means from two populations, which of following assumptions are NOT required?a. The dependent variable scores must be a continuous quantitative variable. b. The scores in the populations are normally distributed. c. Each value is sampled independently from each other value. d. The two populations have similar means22. A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5. 0. The mean score for boys was 65 and the standard deviation of mean was 6. 0. What’s the absolute value of the difference between means?23. A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5. 0. The mean score for boys was 65 and the standard deviation of mean was 5. 0. What is the standard error of the difference in means?24. A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5. 0. The mean score for boys was 65 and the standard deviation of mean was 5. 0. What’s the t-value (two-tailed) for the null hypothesis that boys and girls have the same test scores?25. Which of the following involves making pairwise comparisons?a. Comparing the standard deviation of GRE grades between two statesb. Comparing the variance of the amount of soda consumed by boys and girls in a high schoolc. Comparing the mean weight between children in grades 2, 3, 4 and 5d. Comparing the number of restaurants in New York and Boston26. A professor wanted to test all possible pairwise comparisons among six means. How many comparisons did he need to compare?a. 5b. 6c. 10d. 1527. A professor wants to test all possible pairwise comparisons among three means. If we need to maintain an experiment –wise alpha of 0. 05, what is the error rate per comparison after applying Bonferroni correction?28. Which of the followings can increase the value of t? (select all the apply)a. Increase the standard deviation of difference scoresb. Decrease the standard deviation of difference scoresc. Increase the difference between meansd. Decrease the difference between means29. Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants’ blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there?a. 49b. 50c. 99d. 10030. Which of the followings is the definition of power?a. Power is the probability of rejecting a null hypothesisb. Power is the probability of accepting a null hypothesisc. Power is the probability of accepting a false null hypothesisd. Power is the probability of rejecting a false null hypothesis31. The probability of failing to reject a false null hypothesis is ____a. ?b. 1-?c. 1-?d. ?32. If power is big, you can assume: a. The difference between the means is more likely to be detectedb. The significance level set by the researcher must be highc. We increase the probability of type I errord. Your study result will be more likely to be inconclusive33. If the probability that you will correctly reject a false null hypothesis is 0. 80 at 0. 05 significance level. Therefore, ? is__ and ? is__. a. 0. 05, 0. 20b. 0. 05, 0. 80c. 0. 95, 0. 20d. 0. 95, 0. 8034. As the sample size increases, we assume: a. ? increasesb. ? increasesc. The probability of rejecting a hypothesis increasesd. Power increases35. Which of the following can increase power?a. Increasing standard deviationb. Decreasing standard deviationc. Increasing both means but keeping the difference between the means constantd. Increasing both means but making the difference between the means smallerGeneral Feedback: Power increases if the standard deviation is smaller. If the difference between the means is bigger, the power is bigger.

Umuc Stat200 Quiz 3

Stat 200-Quiz 3 Multiple-choice: Choose only ONE answer in each question. Submit only the answers. There are 27 problems for 80 points total. 01: In a t-test, which of the following does not need to be known in order to compute the p-value? A) knowing whether the test is one-tail or two-tails B) the value of the test statistic C) the level of significance D) the Degrees of Freedom E) none of the above02: As the test statistic becomes larger, the p-value A) becomes smaller B) becomes larger C) becomes negative D) stays the same because the sample size has not been changed E) none of the above03: In a hypotheses testing procedure, ? is the A) Confidence level B) same as the p-value C) 1 – ? D) maximum allowable probability of Type II error E) maximum allowable probability of Type I error 04: The p-value is a probability that measures the support or lack of support for the A) alternative hypothesis B) null hypothesis C) either the null or the alternative hypothesis D) sample statistic E). none of the above05: The average life expectancy of a certain brand of tire has been 40,000 miles. Because of a new manufacturing process introduced it is believed that the life expectancy has increased. To test the validity of this the correct set of hypotheses is A) H0: µ < 40,000 HA: µ ? 40,000 B) H0: µ = 40,000 HA: µ ? 40,000 C) H0: µ > 40,000 HA: µ ? 40,000 D) H0: µ = 40,000 HA: µ < 40,000 E) H0: µ = 40,000 HA: µ > 40,000 06: What kind of Alternative Hypothesis is used in the figure below?A. HA: µ = µ0B. HA: µ ? µ0 C. HA: µ > µ0D. HA: µ < µ0E. none of the above07. Which type of Alternative Hypothesis is used in the figure below?A. HA: µ = µ0B. HA: µ ? µ0C. HA: µ > µ0 D. HA: µ < µ0E. none of the above08: A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. If the machine overfills or under fills then it must be shut down and readjusted. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is A) H0: µ < 12, HA: µ ? 12 B) H0: µ = 12, HA: µ > 12 C) H0: µ ? 12, HA: µ = 12 D) H0: µ = 12, HA: µ ? 12 E) H0: µ = 12, HA: µ < 12Use the following information to do the next four problems. A random sample of 100 people was taken. In the sample 85% favored Candidate Green. We are interested in determining whether or not the proportion of the population in favor of Green is significantly more than 80%. 09: The correct set of hypotheses for this problem is A)H0: p= 0. 85 and HA: p> 0. 85 B)H0: p > 0. 80 and HA: p = 0. 80C)H0: p= 0. 80 and HA: p > 0. 80 D)H0: p= 0. 80 and HA: p ? 0. 80 E)H0: p ? 0. 80 and HA: p > 0. 8010: Find the test statistic. A) 0. 80 B)-1. 25 C) 1. 25 D) 2. 00 E)none of the above11: Find the p-value. A) 0. 1071 B) 0. 8929 C) 0. 8944 D) 0. 1056 E) none of the above12: At the 5% level of significance, can we conclude that the proportion of the population in favor of Green A)is significantly greater than 80% B) is not significantly greater than 80% C) is significantly greater than 85% D) is not significantly greater than 85% E)none of the aboveUse the following information to do the next four problems. The sales of a grocery store had an average of $8,000 per day. The store started an aggressive advertising campaign in order to increase sales. To determine whether or not the advertising campaign has been effective, i. e. the sales increased, a sample of 66 days was selected. For this sample the mean was $8,300 per day and the standard deviation $1,200. 13: The correct Alternative Hypothesis for this problem is A. HA: > 8,000 B. HA: ? 8,000 C. HA: µ > 8,300 D. HA: µ ? 8,000 E. HA: none of the above 14: The value of the test statistic is A) -2. 03 B) 2. 03. C) -2. 00 D) 2. 00 E)none of the above15: The p-value is A) 0. 0248 B) 0. 0228 C) 0. 9752 D) 0. 9768 E) 0. 0232 16: At the 5% level of significance, we conclude that the advertising campaign A)Increased sales B)Decreased sales C)Did not much affect sales D)Was not worth the cost E)None of the aboveUse the following information to do the next five problems. In October the campus bookstore asked a random sample of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. The results of the study are shown below. FreshmenSeniors= $280= 260 = $47= $57 = 80= 8017. Which of the following statements is true?A) This is a two-tail test of two dependent samples. B) This is a two-tail t-test of two independent samples. C) This is a two-tail z-test of two independent samples. D) This is a test of matched pairs. E) None of the above18. To test the claim that the two groups spent the same amount the set of hypotheses isA), B), C), D), E), 19. Find the test statistic z. A) 1. 96B) 1. 645C) 2. 276D) 2. 42 E) 2. 1720. Find the p-valueA) 0. 9922B) 0. 0156 C) 0. 0078D) 0. 0187E)None of the above21. At the 5% level of significance we can concludeA) That the two groups spent the same amounts. B) That the two groups did not spent the same amounts. C) The freshmen spent more. D) The seniors spent more. E) None of the aboveUse the following to answer the next six questions: A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected, the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1and X2 as given in the table. Take d= X1 – X2 = Without booster – With booster. X1 =mileage without boosterX2 =mileage with boosterd=X1-X2d2=(X1- X2)21 21. 223. 82 25. 425. 63 20. 922. 44 27. 628. 35 22. 824. 56 27. 328. 87 23. 425. 2?d =?d2 =d? =You should fill in the table. 22. State the Alternative HypothesisA) B) C) D) E) None of the above23. Compute the mean of the differencesA) -1. 67 B) 6. 3C) 1. 67D) -1. 43 E) None of the above24. Compute the standard deviation of the differencesA) 0. 84 B) 0. 78 C) 0. 13D) 0. 11E) None of the above25. Determine the test statisticA) 4. 85 B) 1. 943C) -3. 96D) -4. 85. E)None of the above26. What is the p-value?A) 0. 0028. B) 0. 0014. C) 0. 0009D) 0. 0001E)None of the above27. At ? = 0. 05 the correct decision and conclusion areA) Reject H0, Booster does not increase mileageB) Reject H0, Booster increases mileage C) Fail to reject H0, Booster does not increase mileageD)Fail to reject H0, Booster increases mileageE)None of the above