The expected value of the sampling distribution of the sample mean is equal to (a) the standard deviation of the sampling population. (b) the mean of the sampling population. (c) the mean of the sample. (d) the population size

*STATS. TRIAL QUESTIONS* *1).* The expected value of the sampling distribution of the sample mean is equal to (a) the standard deviation of the sampling population. (b) the mean of the sampling population. (c) the mean of the sample. (d) the population size *2).* The sample statistic x̄ is the point estimate of (a) the population standard deviation σ. (b) the population median. (c) the population mean μ. (d) the population mode. *3).* For any z distribution, the sum of all the associated z scores will always be (a) equal to 1. (b) less than 1. (c) greater than 1 (d) equal to 0. *4).* A standard normal distribution is a normal distribution with (a) μ=1 and σ=0. (b) μ=0 and σ=1. (c) any mean and σ = 0. (d) any mean and any standard deviation. *5).* The owner of a pawnshop knows that 80 percent of the customers who enter her store will pawn an item. If there are 13 customers in the shop, the probability that at most 6 will pawn an item is (a) 0.006. (b) 0.001. (c) 0.930. (d) 0.007. *6).* A multiple-choice examination has 15 questions. Each question has four possible answers, of which only one is correct. The probability that by just guessing, a student will get exactly 7 correct is (a) 0.039. (b) 0.727. (c) 0.273. (d) 0.561. *7).* The mean number of customers arriving at a bank during a 15-minute period is 10. Find the probability that exactly 8 customers will arrive at the bank during a 15-minute period. (a) 0.0194 (b) 0.1126 (c) 0.0003 (d) 0.0390 *8).* If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be (a) Exponential (b) Poisson (c) Normal (d) None of the above *9).* For a Poisson Distribution, if mean(m) = 1, then P(1) is? (a) 1/e (b) e (c) e/2 (d) Indeterminate *10).* A fair die is rolled until a 2 appears. Find the probability that the first 2 appears on the fifth roll of the die. (a) 0.482 (b) 0.067 (c) 0.0006 (0) 0.080 *11).* The value of Zo such that P(Z ≤ Zo) = 0.8997 is (a) 1.28 (b) 0.00 (c) 0.1003 (d) none of the above *12).* A real estate agent claims that the average price for homes in a certain subdivision is ¢150,000. You believe that the average price is lower. If you plan to test his claim by taking a random sample of the prices of the homes in the subdivision, the formulated set of hypotheses will be (a) Ho: μ ≤ 150,000 vs. Ha: μ > 150,000 (b) Ho: μ = 150,000 vs. Ha: μ ≠ 150,000. (c) Ho: μ < 150,000 vs. Ha: μ ≥ 150,000. (d) Ho: μ ≥ 150,000 vs. Ha: μ < 150,000 *13).* 38. If we are trying to establish that the mean of population 1 is greater than the mean of population 2, the appropriate set of hypotheses is (a) Ho: μ2 - μ1 ≤ 0 vs. Ha: μ2 - μ1> 0 (b) Ho: μ1 - μ2 ≥ 0 vs. Ha: μ1 - μ2 < 0 (c) Ho: μ1 - μ2 = 0 vs. Ha: μ1 - μ2 ≠ 0 (d) Ho: μ1 - μ2 ≤ 0 vs. Ha: μ1 - μ2 > 0 *14).* Which of the following is true? The t distribution should be used when (a) the sampling population is nonnormal. (b) the sampling population is unimodal. (c) the population standard deviation is unknown, the sample size is small, and the sampling distribution is normal. (d) the population standard deviation is known *15).* Commuter students at a certain college claim that the average distance they have to commute to campus is 26 miles per day. A random sample of 16 commuter students was surveyed and yielded an average distance of 31 mi and a variance of 64. The test statistic for this test is (a) z = -2.5 (b) z = 0.0394 (c) t = 2.5 (d) t = 1.25 *16).* If the population proportion is being estimated, the sample size needed in order to be 90 percent confident that the estimate is within 0.05 of the true proportion is (a) 20. (b) 271. (c) 196. (d) 400 *17).* Which of the following confidence intervals will be the widest? (a) 90 percent (b) 95 percent (c) 80 percent (d) 98 percent *18).* A tire manufacturer claims that its tires will last an average of 40,000 miles with a standard deviation of 3,000 miles. Forty-nine tires were placed on test and the average failure miles was recorded. The probability that the average failure miles was more than 39,500 is (a) 0.3790 (b) 0.8790 (c) 0.1210 (d) 0.6210 *19).* A waiter estimates that his average tip per table is $20 with a standard deviation of $4. If his tables seat 9 customers, the probability that the average tip for one table is between $19 and $21 when the tip per table is normally distributed is (a) 0.2734 (b) 0.2266 (c) 0.7734 (d) 0.5468 *20).* If the z score associated with a given raw score is equal to 0, this implies that (a) the raw score equals 0. (b) the raw score does not exist. (c) the raw score is extremely large. (d) the raw score is the same as the mean *21).* Which of the following does not apply to the normal distribution? (a) The normal curve is unimodal. (b) The total probability under the curve is 1. (c) The normal curve is symmetrical about its standard deviation. (d) The mean, the median, and the mode are all equal *22).* The area under any normal curve that is within two standard deviations of the mean is approximately (a) 0.950 (b) 0.680 (c) 0.997 (d) 0.500 *23).* A loan officer has indicated that 80 percent of all loan application forms have zero errors. If 6 forms are selected at random, the probability that exactly 2 of them will have at least one error is (a) 0.150 (b) 0.040 (c) 0.850 (d) 0.246 *24).* A statistics instructor (with at least 20 years' experience teaching the same course) has established that 10 percent of all the students who take his course receive a failing grade. If 10 students have enrolled for his course next semester, the mean number of students who will fail is (a) 1.0 (b) 2.0 (c) 0.5 (d) 20 *25).* The owner of a pawnshop knows that 80 percent of the customers who enter her store will pawn an item. If there are 13 customers in the shop, the probability that at most 6 will pawn an item is (a) 0.006 (b) 0.001 (c) 0.930 (d) 0.007 *26).* If IQ scores are normally distributed with a mean of 100 and a standard deviation of 20, then the probability of a person's having an IQ score of at least 130 (a) is 0.4332 (b) is 0.5000 (c) does not exist. (d) is 0.0668 *27).* The time it takes for a dose of a certain drug to be effective as a sedative on lab animals is normally distributed with a mean of 1 hour and a standard deviation of 0.1 hour. If X represents this time, then P(X > 1.1) is (a) 0.0000 (b) 0.5000 (c) 0.3643 (d) 0.1587 *28).* The area under the standard normal curve between z = -1.68 and z = 0 is (a) 0.4535. (b) 0.0465. (c) 0.9535. (d) -0.4535 *29).* If X is a normal random variable with a mean of 15 and a variance of 9, then P(X < 18) is (a) 0.7486 (b) 0.8413 (c) 0.3413 (d) 0.1587 *30).* If repeated random samples of size 40 are taken from an infinite population, the distribution of sample means (a) will always be normal because we do not know the distribution of the population. (b) will always be normal because the sample mean is always normal. (c) will always be normal because the population is infinite. (d) will be approximately normal because of the Central Limit Theorem *31).* Interval estimates of a parameter provide information on (a) how close an estimate of the parameter is to the parameter. (b) what proportion of the estimates of the parameter are contained in the interval. (c) exactly what values the parameter can assume. (d) the z score. *32).* Suppose the heights of the population of basketball players at a certain college are normally distributed with a standard deviation of 2 ft. If a sample of heights of size 16 is randomly selected from this population with a mean of 6.2 ft, the 90 percent confidence interval for the mean height of these basketball players is (a) 4.555 to 7.845 ft. (b) 5.378 to 7.022 ft. (c) 4.447 to 7.953 ft. (d) 5.324 to 7.077 ft. *33).* The most common confidence levels and the corresponding z values are listed below. Which corresponding z value is incorrect? (a) 99 percent, z value = 1.280 (b) 95 percent, z value = 1.960 (c) 98 percent, z value = 2.330 (d) 90 percent, z value = 1.645 *34).* In a random sample of 150 drunk drivers, 91 percent were males. The 99 percent confidence interval for the proportion of drunk drivers who are male is (a) 0.8716 to 0.9484. (b) 0.8498 to 0.9702. (c) 0.8641 to 0.9559. (d) 0.8555 to 0.9645. *35).* In 1973, the Graduate Division at the University of California, Berkeley, did an observational study on sex bias in admissions to the graduate school. It was found that in a particular major, out of 800 male applicants, 65 percent were admitted, and out of 120 female applicants, 85 percent were admitted. Establish a 95 percent confidence interval estimate of the difference in the proportions of females and males for this particular major. (a) 0.2 ± 0.09 (b) 0.2 ± 0.07 (c) 0.2 ± 0.11 (d) 0.2 ± 0.12 *36).* . If we were testing the hypotheses Ho: μ = μo vs. Ha: μ > μo (where μo is a specified value of μ ) at a given significance level α, with large samples and unknown population variance, then Ho will be rejected if the computed test statistic is (a) Z > Zα (b) Z < -Zα (c) Z > Zα/2 (d) Z < - Zα/2 *37).* An advertising agency would like to create an advertisement for a fast food restaurant claiming that the average waiting time from ordering to receiving your order at the restaurant is less than 5 min. The agency measured the time from ordering to delivery of order for 25 customers and found that the average time was 4.7 min with a standard deviation of 0.6 min. The P value for this test would be (a) 0.100 (b) 0.050 (c) 0.025 (d) 0.010 *38).* An advertising agency would like to create an advertisement for a fast food restaurant claiming that the average waiting time from ordering to receiving your order at the restaurant is less than 5 min. The agency measured the time from ordering to delivery of order for 25 customers and found that the average time was 4.7 min with a standard deviation of 0.6 min. At the 5 percent level of significance, we can claim that the average time between ordering and receiving the order is (a) significantly greater than 4.7 min. (b) significantly smaller than 4.7 min. (c) significantly greater than 5 min (d) significantly smaller than 5 min. *39).* Suppose that a sample of size 100 is selected from a population with unknown variance. If this information is used in constructing a confidence interval for the population mean, which of the following statements is true? (a) The sample must have a normal distribution. (b) The population is assumed to have a normal distribution. (c) Only 95 percent confidence intervals may be computed. (d) The sample standard deviation cannot be used to estimate the population standard deviation because the sample size is large *40).* When will it be reasonable to construct a confidence interval for a parameter if the values for the entire population are known? (a) Never (b) When the population size is greater than 30 (c) When the population size is less than 30 (d) When only lower confidence levels are used *41).* The calculated numerical value that is compared to a table value in a hypothesis test is called the (a) level of significance. (b) critical value. (c) population parameter. (d) lest statistic. *42).* A right-tailed test is performed, with the test statistic having a standard normal distribution. If the computed test statistic is 3.00. the P value for this test is (a) 0.4996. (b) 0.9996. (c) 0.0013. (d) 0.0500. *43).* In testing a hypothesis, the hypothesis that is assumed to be true is (a) the alternative hypothesis. (b) the null hypothesis. (c) the null or the alternative hypothesis. (d) neither the null nor the alternative hypothesis. *44).* New software is being integrated into the teaching of a course with the hope that it will help to improve the overall average score for this course. The historical average score for this course is 72. If a statistical test is done for this situation, the alternative hypothesis will be (a) Ha: p ≠ 72. (b) Ha: p < 72. (c) Ha: p = 72. (d) Ha: p > 72. *45).* A Type I error is defined to be the probability of (a) failing to reject a true null hypothesis. (b) failing to reject a false null hypothesis. (c) rejecting a false null hypothesis. (d) rejecting a true null hypothesis *46).* In hypothesis testing, the level of significance is the probability of (a) failing to reject a true null hypothesis. (b) failing to reject a false null hypothesis. (c) rejecting a false null hypothesis. (d) rejecting a true null hypothesis. *47).* Which of the following general guidelines is used when using the P value to perform hypothesis tests? (a) If the P value > 0.1, there is little or no evidence to reject the null hypothesis. (b) If 0.01 < P value ≤ 0.05, there is moderate evidence to reject the null hypothesis. (c) If the P value ≤ 0.001, there is very strong evidence to reject the null hypothesis. (d) All of the above *48).* If a null hypothesis is rejected at the 0.05 level of significance for a two-tailed test, you (a) will always reject it at the 99 percent level of confidence. (b) will always reject it at the 90 percent level of confidence. (c) will always not reject it at the 99 percent level of confidence. (d) will always not reject it at the 96 percent level of confidence. *49).* The level of significance can be any (a) z value. (b) parameter value. (c) value between 0 and 1, inclusive. (d) α value. *50).* For the following information n=16 μ=15 x̄=I6 σ²=I6 assume that the population is normal. If you are performing a right-tailed test for a single population mean, then (a) P value = 0.3413. (b) P value < 0.05. (c) P value = 0.1587. (d) P value = 0.0794. *51).* For the following information, n=16 μ=15 x̄=I6 σ²=I6 assume that the population is normal. If you are performing a right-tailed test for a single population mean, then you (a) will reject the null hypothesis if α = 0.1. (b) will not reject the null hypothesis if α = 0.1. (c) will not be able to do the test, since more information is needed (d) need the hypotheses to be given. *52).* For the following information, n=16 μ=15 x̄=I6 σ²=I6 assume that the population is normal. If you are performing a left-tailed test for a single population mean, then you (a) will reject the null hypothesis if α = 0.2. (b) will not reject the null hypothesis if α = 0.2. (c) will not be able to do the test, since more information is needed. (d) need the hypotheses to be given. *53).* Dr. J claims that 40 percent of his College Algebra class (a very large section) will drop his course by midterm. To test his claim, he selected 45 names at random and discovered that 20 of them had already dropped long before midterm. The test statistic value for his hypothesis test is (a) 0.6086. (b) 0.3704. (c) 8.3333. (d) 0.6847. *54).* A Type II error is defined to be the probability of (a) failing to reject a true null hypothesis. (b) failing to reject a false null hypothesis. (c) rejecting a false null hypothesis. (d) rejecting a true null hypothesis. *55).* If a null hypothesis is rejected at the 5 percent significance level for a right-tailed test, YOU (a) will always reject it at the 0.1 level of significance. (b) will always reject it at the 0.01 level of significance. (c) will always not reject it at the 0.01 level of significance. (d) will sometimes reject it at the 0.06 level of significance.