1. A researcher believed that there was a difference in the amount of time boys

Question

1. A researcher believed that there was a difference in the amount of time boys and girls in 7th grade exercise. Which of the following was the null hypothesis? a. The amount of hours that boys and girls in seventh grade exercised per day were the same b. The amount of hours that boys at seventh grades exercised per day was greater than the amount of hours that girls in seventh grade exercised per day c. The amount of hours that boys in seventh grades exercised per day was smaller than the amount of hours that girls in seventh grade exercised per day d. The amount of hours that boys in seventh grade exercised per day was bigger than or equal to the amount of hours that girls in 7th grade exercised per day e. None 2. A teacher assumed there was a correlation between amount of hours that his students studied before a history class and their grades. The null hypothesis was that the correlation between the study hours and grades was: a. Positive 1.0 b. Negative 1.0 c. Zero d. Positive 0.50 e. None 3. A professor hypothesized that in a medical school, the students consumed on average 5 or more servings of vegetables every day. If the probability value of her null hypothesis was 0.02, it means: a. We failed to reject the null hypothesis b. The typical student consumed 5 or more servings of vegetables every day c. Every student consumed more than 5 serving of vegetables every day d. Her null hypothesis was rejected e. None Page 2 of 10 4. A student hypothesized that there was no significant difference between men and women on a standardized math test. The probability value for his null hypothesis was 0.30. So he concluded that: a. Women achieved significantly better scores on the standardized math test than men b. Women achieved significantly worse score on the standardized math test than men c. Women achieved much better scores on the standardized math test than men d. He could not reject the null hypothesis e. None 5. At which of the following significance levels do you feel the most confident to reject the null hypothesis? a. 0.05 b. 0.01 c. 0.95 d. 0.99 e. None 6. A student hypothesized that in his class, the average weight was 120 lbs. If the 95% confidence interval of weights of all students was (90, 115), can you reject the null hypothesis that the mean weight was equal to 120 lbs at 0.05 level? a. Yes b. No c. We cannot tell from the given information 7. A teacher hypothesized that the on average, his students consumed two bottles of soda per day. Imagine that the teacher recorded soda consumption for every student: the confidence interval of soda consumption was (1.6, 2.4). Can you reject the teacher’s null hypothesis at 95%? a. Yes b. No c. We cannot tell from the given information 8. If a 95% confidence interval contains 1, does that mean its 99% confidence interval contains 1? a. Yes b. No c. We cannot tell from the given information 9. If a statistical test result is significant at the 0.01 level, then we can conclude: a. It is not significant at 0.05 level b. It is not significant at 0.10 level c. We do not know if it will be significant at 0.05 level d. It must be significant at 0.05 level e. None Page 3 of 10 10. ___ is the probability of accepting a false null hypothesis. a. 1- b. c. d. 1- e. None 11. Significance level is equal to: a. b. c. 1- d. 1- e. None 12. A professor wanted to test all possible pairwise comparisons among five means. How many comparisons did he need to compare? a. 5 b. 6 c. 10 d. 15 e. None 13. A researcher wanted to compare the blood sugar level before and after breakfast among the same population. There were 100 participants in this study. The researcher measured their blood sugar level 30 minutes before breakfast and then he measured their blood sugar level again 30 minutes after breakfast. If he wanted to compare the mean blood sugar before and after breakfast by using a two-tailed t test, how many degrees of freedom were there? a. 99 b. 100 c. 199 d. 200 e. None 14. Power is defined as ____ a. b. 1- c. 1- d. e. None 15. 1- is the probability of_______ a. Rejecting a true null hypothesis b. Accepting a true null hypothesis c. Accepting a false null hypothesis d. Rejecting a false null hypothesis e. None Page 4 of 10 16. Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is: a. p < 0.30 b. p 0.30 c. p 0.30 d. p > 0.30 e. None 17. A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________. a. at least 20%, when in fact, it is less than 20%. b. 20%, when in fact, it is 20%. c. less than 20%, when in fact, it is at least 20%. d. less than 20%, when in fact, it is less than 20%. e. None 18. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: a. Ho: x = 4.5, Ha : x > 4.5 b. Ho : 4.5, Ha : < 4.5 c. Ho : = 4.75, Ha : > 4.75 d. Ho : = 4.5 Ha : > 4.5 e. None 19. Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91, respectively. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The “day” subscript refers to the statistics day students. The “night” subscript refers to the statistics night students. An appropriate alternative hypothesis for the hypothesis test is: a. day > night b. day < night c. day = night d. day night e. None Page 5 of 10 20. The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals. Western Eastern Los Angeles 9 D.C. United 9 FC Dallas 3 Chicago 8 Chivas USA 4 Columbus 7 Real Salt Lake 3 New England 6 Colorado 4 MetroStars 5 San Jose 4 Kansas City 3 Table A The exact distribution for the hypothesis test is: a. the normal distribution b. the Student's t-distribution c. the uniform distribution d. the exponential distribution e. None PART II: Problem-Solving—Solve each of the following problems. (40 points – 10 pts each) 1. Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter ( or p). a. The mean number of years Americans work before retiring is 34. ____________________________________ b. At most 60% of Americans vote in presidential elections. ____________________________________ c. The mean starting salary for San Jose State University graduates is at least $100,000 per year. ____________________________________ d. Twenty-nine percent of high school seniors get drunk each month. ____________________________________ e. Fewer than 5% of adults ride the bus to work in Los Angeles. ____________________________________ f. The mean number of cars a person owns in her lifetime is not more than ten. ____________________________________ g. About half of Americans prefer to live away from cities, given the choice. ____________________________________ h. Europeans have a mean paid vacation each year of six weeks. ____________________________________ i. The chance of developing breast cancer is under 11% for women. ____________________________________ j. Private universities' mean tuition cost is more than $20,000 per year. ____________________________________ Page 6 of 10 2. A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. a. Is this a test of means or proportions? b. State the null and alternative hypotheses. H0: _________________ Ha: ______________ c. Is this a right-tailed, left-tailed, or two-tailed test? ____________________________________ d. What symbol represents the Random Variable for this test? ____________________________________ e. In words, define the random variable for this test. ____________________________________ f. Is the population standard deviation known and, if so, what is it? ____________________________________ g. Calculate the following: i. x = _____ ii. s =_____ iii. n =_____ h. Which test should be used? ____________________________________ i. State the distribution to use for the hypothesis test. ____________________________________ j. Find the p-value. ____________________________________ k. At a pre-conceived = 0.05, what is your: i. Decision: ____________________________________ ii. Reason for the decision: ____________________________________ iii. Conclusion (write out in a complete sentence): ____________________________________ Page 7 of 10 3. The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population. a. Is this a test of one mean or proportion? ____________________________________ b. State the null and alternative hypotheses. H0: ____________________ Ha: ____________________ c. Is this a right-tailed, left-tailed, or two-tailed test? ____________________________________ d. What symbol represents the random variable for this test? ____________________________________ e. In words, define the random variable for this test. ____________________________________ f. Calculate the following: i. x = ________________ ii. n = ________________ iii. p = _____________ g. Calculate x = __________. Show the formula set-up. ____________________________________ h. State the distribution to use for the hypothesis test. ____________________________________ i. Find the p-value. ____________________________________ j. At a pre-conceived = 0.05, what is your: i. Decision: ____________________________________ ii. Reason for the decision: ____________________________________ iii. Conclusion (write out in a complete sentence): ____________________________________ Page 8 of 10 4. The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. a. Is this a test of means or proportions? __________________________ b. State the null and alternative hypotheses. H0: _________________ Ha: ______________ c. Is this a right-tailed, left-tailed, or two-tailed test? ____________________________________ d. What symbol represents the Random Variable for this test? ____________________________________ e. In words, define the random variable for this test. ____________________________________ f. Is the population standard deviation known and, if so, what is it? ____________________________________ g. Calculate the following: i. x = _____ ii. s =_____ iii. n =_____ h. Which test should be used? ____________________________________ i. State the distribution to use for the hypothesis test. ____________________________________ j. Find the p-value. ____________________________________ k. At a pre-conceived = 0.05, what is your: i. Decision: ____________________________________ ii. Reason for the decision: ____________________________________ iii. Conclusion (write out in a complete sentence): ____________________________________ Page 9 of 10 PART III: Problem-Solving—Solve each of the following problems. (20 points – 5 pts each) 1. The mean age of graduate students at a University is at most 31 years with a standard deviation of two years. A random sample of 15 graduate students is taken. The sample mean is 32 years and the sample standard deviation is three years. Are the data significant at the 1% level? The p-value is 0.0264. State the null and alternative hypotheses and interpret the p-value. H0: _______________________________ Ha: _________________________________ Interpret the p-value: _________________________________________________________________________ 2. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table B H0: _______________________________ Ha: _________________________________ What is the test statistic?______________________________________ What is the p-value?______________________________________ 3. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table C shows the result. Scouters believe that Rodriguez pitches a speedier fastball. Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation Wesley 86 3 Rodriguez 91 7 Table C H0: _______________________________ Ha: _________________________________ What is the test statistic?______________________________________ What is the p-value?___________________________________________ Page 10 of 10 4. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. H0: _______________________________ Ha: _________________________________ What is the test statistic?______________________________________ What is the p-value?_________________________________

Explanation / Answer

1.

OPTION A: a. The amount of hours that boys and girls in seventh grade exercised per day were the same [ANSWER]

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2.

By definition,

OPTION C: c. Zero [ANSWER]

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3.

OPTION E: None

This is so because we do not know the significance level. It depends on the significance level whether a P value of 0.02 is low enough to Reject Ho or not.

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4.

d. He could not reject the null hypothesis [ANSWER]

As P value of 0.30 is too big, so we cannot reject Ho.

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