Math 116 Exam 3: Confidence Intervals and Hypothesis Testing - Interpreting Results - Prof, Exams of Statistics

Download Math 116 Exam 3: Confidence Intervals and Hypothesis Testing - Interpreting Results - Prof and more Exams Statistics in PDF only on Docsity! Math 116 – Practice Exam 3 – Group Work - Confidence Intervals and Hypothesis Testing -Interpreting Results The results will be given to you. You have to interpret the results and write the conclusion using words within the context of the problem. In the hypothesis testing problems indicate what number in the output helped you reach the conclusion. Refer to the likelihood of the point estimate in your explanations. Also indicate whether they are significantly lower/higher/different or they are lower/higher/different by chance. In the confidence interval problems, you must be very specific in your answer of what the interval suggests. 1 Math 116 – Exam 3 – Practice Group work Your Name____________________ Confidence Intervals and Hypothesis Testing -Interpreting Results - This part will count for 10% of your exam 3 grade. 1) In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Twenty-eight computer components were selected at random and the mean time between failures was 529.2 with a standard deviation of 15.2. At the 5% significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. Assume that the population is normally distributed. THIS PROBLEM HAS BEEN SOLVED BY USING THE CALCULATOR. A 90% CONFIDENCE INTERVAL IS ALSO SHOWN. ALL QUESTIONS ARE LISTED BELOW THE RESULTS. a) IN EACH OF THE FOLLOWING STATEMENTS, CIRCLE THE CORRECT CHOICE &COMPLETE THE BLANKS. (1) We REJECT / FAIL TO REJECT Ho (2) Test results ARE NOT / ARE statistically significant at the 5% level (3) At the 5% significance level, we SUPPORT / DO NOT HAVE ENOUGH EVIDENCE TO SUPPORT the claim that, after the modification, the mean time between failures is higher than 520 hours (4) If the mean of the population is 520 hours, the likelihood of observing a sample mean of 529.2 or a higher one is ____________ This means, it’s USUAL / UNUSUALto observe a sample mean of 529.2 hours when the population mean is 520 hours. (5) x-bar = 529.2 is SIGNIFICANTLY HIGHER / HIGHER BY CHANCE than mu = 520 (6) The point estimate for mu is ______________ (7) The margin of error is ___________________ (Using the interval results, show here how you find it) (8) With _______% confidence we can say that after the modification, the mean time between failures is _________hours with a margin of error of _____________ b) The confidence interval suggests that μ could be = 520 μ < 520 μ > 520 Based on the interval results, EXPLAIN YOUR CHOICE c) Do you think the modification worked? YES NO EXPLAIN 2 experimental group) received Accupril. The 579 subjects in Group 2 (the control group) received a placebo. Of the 1563 subjects in the experimental group, 61 experienced dizziness as a side effect. Of the 579 subjects in the control group, 15 experienced dizziness as a side effect. At the 2.5% significance level, use the test results given below to test the claim that the proportion experiencing dizziness in the experimental group is greater than that in the control group. A 95% confidence interval has also been constructed. What conclusions can be drawn from the clinical trials? a) Give your conclusion based on the hypothesis testing results b) How do the confidence interval results support your conclusion written in part (a)? c) Do we have enough evidence to say that dizziness is a side effect of the drug Accupril? YES NO MUST EXPLAIN d) Show here how you find the following. (Do not use the long complicated formulas from the chart – There is no time for that) The point estimate for p1 – p2 is___________________ The margin of error is_______________ 5 DO THIS AFTER YOU FINISH ALL OTHER PAGES Your name___________________________ 7) Show how you find the test statistic in problem 1 (THE TEST STATISTIC IS THE Z-SCORE) (Use formulas from chapter 7) 8) Show how you find the confidence interval in problem 1 (Use formulas) 9) Show how you find the test statistic in problem 2 (THE TEST STATISTIC IS THE Z-SCORE) (Use formulas from chapter 7) 10) Show how you find the p-value in problem 2 (this involves the z-chart) 11) Show how you find the confidence interval in problem 2 (Use formulas) 6