# MATHEMATICS

Question 27 Assume a normal distribution. A coin is tossed 100 times. Find the probability of 52 to 65 heads. Round your percentage to the hundredths place. 38.11% 32.45% 42.11% 36.45% Question 28 Which statement is correct? 1. A point estimate is a single number that has been calculated to estimate the population parameter. 2. A point estimate is an estimate of the range of values for which an unknown, but true sample statistic lies. 3. A point estimate is a sample statistic such that the mean of all possible values equals the population parameter. 4. A point estimate is the sum of an estimator’s squared bias plus its variance. Statement A Statement B Statement C Statement D Quesrion 29 Which statement is correct? 1. An interval estimate is a sampling procedure that matches each unit from Population A to a corresponding unit from Population 2. An interval estimate is an estimate of the range of values for which an unknown, but true sample statistic lies. 3. An interval estimate is a sample statistic such that the mean of all possible values equals the population parameter the statistic seeks to estimate. D. An interval estimate is the sum of an estimator’s squared bias plus its variance Statement A Statement B Statement C Statement D

Question 30 A proportion of a college basketball team’s season ticket holders renew their tickets for the next season. Let ‘p’ denote the true proportion of ticket holders who buy tickets again for the following season. A random sample of 132 ticket holders revealed 93 people plan on renewing their tickets. Find the point estimate for ‘p’. 1.419354839 0.7045454545 0.2954545455 0.8345454545 0.4193548387 Question 31 Which statement is not correct? A. The Central Limit Theorem of a sample proportion ‘p’ indicates that the mean of the sampling distribution of ‘p’ will be equal to the population proportion p. B. The Central Limit Theorem of a sample proportion ‘p’ indicates that the sampling distribution of ‘p’ can be approximated by a normal distribution is np > 5 and nq > 5. C. The Central Limit Theorem of a sample proportion ‘p’ is applied regardless of the sample size n and the population proportion p. D. The Central Limit Theorem of a sample proportion ‘p’ is applied to non-normal populations. Statement A Statement B Statement C Statement D

Question 32 Which of the following sample sizes will produce a sampling distribution of the mean that is approximately normal? 10 20 30 All of the above. Consider a large population with a mean of 150 and standard deviation of 27. A random sample of size 36 is taken from the population. Calculate the standard error of the sampling distribution of this sample mean and round your answer to the hundredths place. 5.10 4.80 4.60 4.20

Question 34 Compute the margin of error in estimating a population mean for a sample size of 6000 and a variance of 9. Round your answer to the thousandths place. 0.076 0.240 0.506 0.759

Question 35 If the standard deviation of a population is known and we wish to estimate the population mean with 98% confidence, what is the appropriate critical value ‘z’ to use? 2.58 2.33 1.96 1.645 1.28 Question 36 What does the interpretation of a 90% confidence interval estimate mean? If we repeatedly draw samples of the same size from the same population, 90% of the values of the sample means will result in a confidence interval that includes the population mean There is a 90% probability that the population mean will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL). We are 90% confident that we have selected a sample whose range of values does not contain the population mean. There is a 10% probability that the population mean will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL). If we repeatedly draw samples of the same size from the same population, 10% of the values of the sample means will result in a confidence interval that includes the population mean.

Question 37 A random sample of 56 salespersons were asked how long on average they were able to talk to a potential customer. Their answers revealed a mean of 8.100000000 with a variance of 6 minutes. Construct a 95% confidence interval for the time it takes a salesperson to talk to a potential customer. LCL = 8.058439402, UCL = 9.841560598 LCL = 7.458439402, UCL = 8.741560598 LCL = 6.958439402, UCL = 10.24156060 LCL = 7.958439402, UCL = 10.34156060 LCL = 6.858439402, UCL = 8.041560598

Question 38 A random sample of 74 people revealed it took an average (mean) of 60 minutes with a standard deviation of 10 minutes for a person to complete a loan application at the bank. Construct a 90% confidence interval for the true time it takes any person to complete a loan form. LCL = 57.58772634, UCL = 63.41227366 LCL = 57.48772634, UCL = 61.21227366 LCL = 58.68772634, UCL = 63.01227366 LCL = 58.08772634, UCL = 61.91227366 LCL = 58.58772634, UCL = 63.51227366

Question 39 A statistical test of hypothesis consists of the five parts below. Place the parts in order, beginning with the first part. 1. State the conclusion. 2. Calculate the test statistic and its p-value. 3. Determine the alternate hypothesis. 4. Determine the null hypothesis. 5. Determine the rejection region. A, B, C, D, E D, C, A, B, E C, D, B, E, A D, C, B, E, A D, C, E, B, A