Matt Jones MATH 1530 Elements of Statistics Exam III NAME You have the class period to complete this exam You may use 1 a writing utensil 2 a calculator 3 one 8 5 11 page of notes 4 normal or t tables as needed To receive full credit you must show and do your own work YOU MAY NOT SHARE ANY OF THE ABOVE MATERIALS Good Luck The first 12 questions are multiple choice and pertain to confidence intervals and hypothesis tests for a population mean Choose the very best answer 1 The margin of error is a twice the width of a confidence interval b the width of a confidence interval c half the width of a confidence interval d 1 standard deviation e 2 standard deviations 2 As the sample size decreases a confidence interval tends to a increase in width b decrease in width c keep the same width d shift to the right e shift to the left 3 Increasing the confidence level a decreases the margin of error b increases the sample mean c decreases the sample mean d increases the width of the confidence interval e decreases the width of the confidence interval 4 Decreasing the sample mean a decreases the margin of error b increases the margin of error c shifts the interval to the left d shifts the interval to the right e increases the chance of making type IV error 5 Which statement s are correct i 95 of all 95 confidence intervals contain the actual population mean ii A 95 confidence interval contains 95 of the data iii The sample mean is the midpoint of a confidence interval a i only b i and ii only c i ii and iii d ii and iii only e i and iii only 6 In a hypothesis test if the p value is low you should a accept the null hypothesis b reject the alternative hypothesis c do it again because a type I error has been made d reject H0 e do it again because a type II error has been made 7 In practice a t intervals and t tests are usually made because the population standard deviation is usually known b z intervals and z tests are usually made because the population standard deviation is usually known c t intervals and t tests are usually made because the population standard deviation is usually unknown d z intervals and z tests are usually made because the population standard deviation is usually unknown e z intervals and z tests are usually made because of the central limit theorem 8 The p value is a the probability of observing a test statistic value as extreme as the one calculated from the sample b the probability of type I error c the probability of failing to reject the null hypothesis when the null hypothesis is true d the probability of failing to reject the null hypothesis when the null hypothesis is false e the probability of type II error 9 When doing a hypothesis test it is important to a check if data could be coming from a population that is normally distributed b take as large a sample as possible c take a simple random sample d all of the above e none of the above 10 As the degrees of freedom increase t 2 gets a closer to t b closer to z c farther from z 2 d farther from t 2 e closer to z 2 11 Type I error occurs when a we fail to reject H0 in favor of Ha when H0 is true b we fail to reject H0 in favor of Ha when Ha is true c we reject H0 in favor of Ha when H0 is true d we reject H0 in favor of Ha when Ha is true e we reject H0 and Ha in favor of the test statistic 12 Recall the value of the t test statistic is t0 x 0 s n When doing a right tailed t test a large positive values of t0 correspond to large p values b large positive values of t0 correspond to small p values c we should reject H0 in favor of Ha if t0 is near 0 d we should fail to reject H0 if t0 is large e large negative values of t0 correspond to small p values 13 Examine the following dotplots and summary statistics Sample Mean StDev 1 17 20 1 656 2 17 20 5 44 3 14 20 1 656 4 13 674 0 674 Which of the following statements is are true i Sample 1 has more evidence than Sample 2 that the population mean is not 19 ii Sample 3 has more evidence than Sample 2 that the population mean is not 19 iii Sample 4 has more evidence than any of the other samples that the sample mean differs from 19 a i only b i and ii only c ii and iii only d i and iii only e all are true 14 Calculate the following and round correctly at the third decimal place a For a confidence level of 95 z 2 b For a confidence level of 98 z 2 c For a confidence level of 95 and sample size n 10 t 2 d For a confidence level of 98 and sample size n 8 t 2 15 The average number of dart throws it took 81 randomly chosen people to get a bullseye was 42 7 with a sample standard deviation of 16 5 a Are the assumptions for making a t interval satisfied Explain Be sure to address each assumption b Construct a 95 confidence interval for the actual mean number of dart throws required to get a bulleye Show your work for full credit Also make sure to interpret the interval in a complete sentence 16 The Hando Car Company wants you to make a 98 confidence interval for the average damage done in to its vehicles when Bad Brad their careless driver transports them from the factory to the dealership They want this interval to be no more than 300 in width Based on company records they believe the standard deviation of damages to be about 400 What is the minimum required number of cars that must be sampled Show your work for full credit 17 The average GPA of students at a university in the year 2000 was 2 6 The registrar wants to see if the mean GPA has increased The mean and sample standard deviation of a simple random sample of 91 students GPAs were 2 7 and 0 4 respectively a Are the assumptions for doing a right tailed t test satisfied Explain Be sure to address each assumption b State the null and alternative hypotheses c Calculate the p value Show your work for full credit d Based on your answer to the previous part the registrar can probably conclude i ii iii iv v The mean GPA has not changed The mean GPA has increased some The mean GPA has decreased by a ton Like about a letter 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