MATH 203 Test 2 Review Problems: Statistical Inference and Confidence Intervals, Exams of Statistics

Download MATH 203 Test 2 Review Problems: Statistical Inference and Confidence Intervals and more Exams Statistics in PDF only on Docsity! MATH 203 Test 2 Review Problems Part 1: Short Answer – No Calculators 1. Let 1 be the average lifetime (in hours) of Type 1 batteries and let 2 be the average lifetime of Type 2 batteries. A 95% confidence interval found that –1.55 ≤ 1 − 2 ≤ 0.86. (a) Use this interval to express a comparison of the average lifetimes of these two types of batteries. (b) Which type of battery has the longer average lifetime? ______________________________________________________________________________ 2. Let p1 be the true proportion of patients who have worsening of their condition with Treatment A, and p2 be the true proportion of patients who have worsening of their condition with Treatment B. A 95% confidence interval found that –0.052 ≤ p1 – p2 ≤ –0.024 . (a) Use this interval to give a comparison between the percentages of patients who have a worsening of their condition. (b) Which treatment has the higher percentage of patients with a worsening of the condition? ______________________________________________________________________________ 3. The city mileage of a certain automobile is normally distributed with a standard deviation of = 2 mpg. It is thought that the mean is about 25 mpg. But a testing of 400 such automobiles gave x = 24.2 and S = 1.8. Test if the sample gives significant evidence to conclude that the mean mpg is not 25. Results from a one-sided Z–Test and a one-side T–Test are shown: (a) State the null hypothesis and an appropriate one-sided alternative. (b) Which test do you use and why? (c) Show how to find the test statistic. (d) Use the appropriate P -value from above to explain your conclusion in detail. (e) With = 0.05, what is the endpoint of the rejection region for your one-sided test in Part (a)? Graph it and state the distribution curve used. What if = 0.025? (f) Suppose that the mpg is not normally distributed or that we do not know that . Why can we still use the same test as in Part (b)? ______________________________________________________________________________ 4. In Mexico, birth weights are normally distributed with unknown standard deviation. A sampling of 36 recent births gave a sample mean weight of 6.3 lbs. with a sample deviation of 1.5 lbs. We wish to see if there is significant evidence to conclude that the mean birth weight in Mexico differs from 6 lbs. Results from a one-sided Z–Test and T– Test on the sample are given below. (a) State the null hypothesis and alternative. (b) Which test do you use and why? (c) Use the appropriate P -value from above to explain your conclusion in detail. (d) Find the endpoint of the rejection region for your one-sided test using = 0.05. Show it on a shaded graph and state the distribution curve used. t-scores 0.90 0.95 0.98 0.99 deg. of fr. 34 1.691 2.032 2.441 2.728 35 1.690 2.028 2.438 2.724 36 1.688 2.028 2.434 2.719 (e) Show how to find the test statistic used for your test in Part (a). Explain the conclusion in terms of the test statistic. ______________________________________________________________________________ 5. A politician claims that 60% of adults support raising taxes on the rich. But a Gallup Poll found that 630 out of 1000 adults (63%) had this belief. Test if this poll gives good evidence that more than 60% of all adults favor raising taxes on the rich. (a) State the null hypothesis and an appropriate one-sided alternative. (b) Show how to find the test statistic. (c) If we use a 5% level of significance, then what endpoint gives the bound for rejecting the null hypothesis? Graph it and state the distribution curve used. What if we use a 2.5% level? (d) Use the appropriate P -value from above to explain the conclusion in detail based upon a 0.05 level of significance. (e) Use the test statistic to explain whether or not we have evidence to reject H0 with a 0.025 level of significance.