Math 243: Final Exam - Significance Testing and Hypothesis Testing - Prof. Fred Hervert, Exams of Probability and Statistics

Download Math 243: Final Exam - Significance Testing and Hypothesis Testing - Prof. Fred Hervert and more Exams Probability and Statistics in PDF only on Docsity! Practice Math 243 Final Note: much of this was provided by Fred Hervert and Ben Dominik 1. [] TRUE/FALSE: Circle T in each of the following cases if the statement is always true. Otherwise, circle F. Let f be a function, and x, y, and z be positive real numbers with z 6= 0. T F A 95% confidence interval contains the populations mean or proportion that is being sought. T F If the null hypothesis is not rejected at the significance level of .05, it will always be rejected at the .1 level. T F If a null hypothesis is rejected at a significance level of .05, it will always be rejected at the .01 level. T F The mean is not greatly affected by outliers. T F If the P-value is greater than the level of significance for a test, then we accept the null hypothesis. T F A correlation of 0 means that there is a linear pattern between the explanatory and response variables. Show your work for the following problems. The correct answer with no supporting work will receive NO credit. 2. Explain the reasoning behind significance testing. Include examples. 3. Every term I receive evaluations from my students and included in my summary is a z-score. One question on the evaluation from Spring of 2007 term was “How available was the instructor during office hours?” with a corresponding z-score of -1.1. Explain what this means. 4. In a large Midwestern university (the class of freshmen being on the order of 36,000 or more students), an SRS of 100 entering freshmen in 1988 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1990. In 1992 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. The administration would like to know if there Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 1992 has been reduced as a result of the tougher admission standards adopted in 1990, compared to the proportion in 1988 1 (a) What kind of significance test are you going to use? (b) Perform the test and find the associated P-value. (c) Explain what the P-value is in the context of this problem. (d) Conclude using the context of this problem. (e) Do you believe your conclusions? 5. In 1952, the Gallup poll predicted that Eisenhower would win the election with 51.0% of the vote. This was based on a sample of size 5,385. (a) What kind of procedures are you about to use? (b) Find a 99% confidence interval for the percent of the population voting for Eisen- hower according to this poll. (c) In the election, Eisenhower actually received 55.4% of the vote. Test whether this is a likely value for the true proportion voting for Eisenhower based on this sample. 6. A pollster reports that he is 99% confidence that 58% of voters favor a certain candidate in the upcoming presidential election with a margin of error of 6%. (a) What was the sample size? (b) What should the sample size be so that the 99% confidence interval for the pro- portion of voters favoring this candidate has a margin of error of 2%? (c) If the pollster reports that based on a sample of size 3,000, he predicts that the candidate will win 58% of the vote with a margin of error of 2.096%, what confidence does he have in the prediction? 7. A simple random sample collected the following data. height (feet) 3.5 3.6 3.4 5 5.3 4.7 5.5 5.3 5.7 IQ score 87 100 94 115 120 112 114 107 128 (a) Which is the explanatory (or independent) variable and which is the response (or dependent) variable? (b) Draw a scatterplot of the data. Label the axes appropriately. (c) Find the equation of the regression line and plot it on your scatterplot. (d) Find the correlation for the data and explain how strong the relationship between the two variables is. (e) Explain why you see the relationship that you do between the two variables. 8. An experiment is conducted to compare the starting salaries of a random collection of male and female graduates from a large midwestern university. Male and female students are paired if they have a similar major and similar GPA’s. The following table summarizes the results: 2