2003 final - STATISTICS 2023 FINAL EXAM FALL 2003 NAME,...

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Unformatted text preview: STATISTICS 2023 FINAL EXAM FALL 2003 NAME, PRINT IN INK______________________________ SIGNATURE, IN INK_______________________________ SS or OSU ID #, IN INK_____________________________ (3 points each) TRUE OR FALSE. Answer with a capital T or F. ______ 1. If the z score is -1.5 for an individual data value from a population with mean of 25 and standard deviation of 6 then the individual data value is equal to 16. ______ 2. Continuous random variables have probability only on specific values of the variables. ______ 3. The probability density function for the normal distribution is a left skewed distribution with only positive values. ______ 4. The point estimate for the population mean is the center of a confidence interval to estimate the population mean. ______ 5. The p-value in a hypothesis test is the tail area associated with the rejection region of the hypothesis test and is set by the researcher before the data are collected. ______ 6. The t-multiplier in the bound of error for a 99% confidence interval to estimate the mean of a population with unknown variance based on only 10 observations would be the value 2.821, not 3.250. ______ 7. If a null hypothesis is true, then the distribution of the test statistic is known and the p-value measures the likelihood of a test statistic at least as extreme as the one calculated from the data. STATE THE ANSWER. Write the answer on the line. ______________ 8. What is the P(t > 3.610) if df = 18? (3 points each) ______________ 9. State the value of to, if the P(t > to) = .95 and the df = 26. _____________ 10. What is the P( - 2.821 < t < 2.821) if df = 9? STATISTICS 2023 FINAL EXAM FALL 2003 STATE THE ANSWER. Write the answer on the line. PAGE TWO (3 points each) _______________ 11. If a 95% confidence interval based on a large sample to estimate a population mean is (129.21, 172.33) then what is the value of the standard error of the point estimate for the population mean? _______________ 12. If a two-tail hypothesis test on the population mean based on a large sample provides a test statistic value of – 0.47 what is the p-value of the hypothesis test? _______________ 13. If the rejection region in a left-tail hypothesis test based on a large sample is below –1.96 what is the maximum error rate of rejecting a true null hypothesis that this researcher will tolerate? _______________ 14. In a right-tail hypothesis test based on a random sample of 18 observations the null hypothesis would be rejected at the error rate of 0.001 if the t test statistic is greater than what value? ________________15. If a researcher who is comparing the means of two populations is attempting to prove that the mean of population two is more than 2 units larger than the mean of population one what is the appropriate alternative hypothesis? ________________16. If the mean of the sample from population one is 42.3 and the mean of the sample from population two is 84.8 what is the numerical value of the point estimate for the mean of population one minus the mean of population two? ________________17. If a sample of 22 observations had a sample variance of 4.5 and a sample of 15 observations had a sample variance of 5.6 then what is the numerical value of the pooled variance estimate based on these two samples? State two digits past the decimal. STATISTICS 2023 FINAL EXAM FALL 2003 STATE THE ANSWER. Write the answer on the line. PAGE THREE (3 points each) The response times to emergency maintenance problems at an assembly plant for 8 randomly selected emergency calls are as follows, in hours. 1.22 1.88 2.33 4.17 1.51 2.70 2.18 3.77 _______________ 18. What is the numerical value of the point estimate for the population mean? State two digits after the decimal. _______________ 19. What is the numerical value of the point estimate for the population variance? Round your answer to three digits past the decimal. ________________20. Assume that the estimated standard error of the point estimate for the population mean is 0.25. What is the numerical value of the test statistic to test if the mean response time to emergency maintenance problems is equal to 2? State two digits past the decimal. HYPOTHESIS TEST QUESTIONS In order to compare the means of two populations, independent random samples selected from two normal populations produced the sample means and standard deviations shown below: (assume equal population variances) Sample 1 Sample 2 n1 = 6 n2 = 12 x1 = 8.6 x2 = 5.8 s1 = 1.8 s2 = 1.4 ________________ 21. What is the numerical value of the point estimate for the difference between the means for these two samples? ________________ 22. What is the numerical value of the pooled variance estimator based on the two samples of data? State two digits after the decimal. ________________ 23. What is the appropriate alternative hypothesis if the research question is, “Do the data indicate that the mean of population one is more than 1 unit greater than the mean of population two? ________________ 24. What is the numerical value of the test statistic that would be used to attempt to support the alternative hypothesis described in the above question? Round your answer to two digit past the decimal. ________________ 25. Assume that the value of the test statistic in this situation was 2.4 then the p-value associated with the test statistic value would be between what two values? STATISTICS 2023 FINAL EXAM FALL 2003 LINEAR REGRESSION QUESTIONS. Write the answer on the line. PAGE FOUR (3 points each) Consider the following pairs of measurements. Use this data to answer the next three questions. x96463538 y23637254 _______________ 26. What is the numerical value of the least squares estimate of the slope from the data above? Round your answer to three digits past the decimal. _______________ 27. What is the numerical value of the least-squares estimate of the yintercept from the data above? Round your answer to one digit past the decimal. _______________ 28. What is the numerical value of the estimated linear correlation from the data above? Round your answer to one digits past the decimal. ANOTHER LINEAR REGRESSION QUESTION. Assume that linear regression has been used by a manufacturing company to estimate total production cost, y, with an equation based on labor cost, x. The least squares estimated regression equation resulting from the bivariate data set is listed below. Use this information to answer the next five questions. ˆ y = 9 8 1 + 4 .7 6 x _______________ 29. What is the numerical value of the least squares estimate of the y-intercept? _______________ 30. What is the numerical value of the least squares estimate of the slope? _______________ 31. What is the estimate of total production cost if the labor cost is $800? _______________ 32. How much does total production cost increase if labor cost increases by $100? _______________ 33. If the standard error of the least squares estimate of the slope is 1.19 what is the numerical value of the test statistic to test if the slope is equal to zero? ...
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This note was uploaded on 04/25/2010 for the course STA 2023 taught by Professor Ripol during the Spring '08 term at University of Florida.

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