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##### stats MCQ problems with solution fall 2014

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Question;1The right way to think about the sample mean is:a The sample mean is a constant number.b The sample mean is a different value in each random sample from the population mean.c The sample mean is always close to the population mean.d The sample mean is always smaller than the population mean.2The sampling distribution of x is approximately normal ifa the distribution of x is skewed.b the distribution of x is approximately symmetricc the sample size is large enough.d the sample size is small enough.3abcdThere is a population of six families in a small neighborhood: Albertson, Benson, Carlson,Davidson, Erikson, and Fredrickson. You plan to take a random sample of n=3 families (withoutreplacement). The total number of possible sample is _____.6121820abcdThe mean daily output of an automobile manufacturing plant is = 520 cars with standarddeviation of = 14 cars. In a random sample of n = 49 days, the probability that the samplemean output of cars (x) will be within 3 cars from the population mean is _________.0.98760.95440.92660.8664abcdIn the population of IUPUI undergraduate students 38 percent (0.38) enroll in classes during thesummer sessions. Let p denote the sample proportion of students who plan to enroll in summerclasses in samples of size n = 200 selected from this population. The expected value of thesample proportion, E(p), is _______.0.380.280.250.18abcdIn the previous question, the standard error of the sampling distribution of p is, se(p)=_______.0.03430.02970.02480.02214567The expressionMeans:a Once you take a specific sample and calculate the value of x, the probability that the value of xyou just calculated is within 1.96 /n from is 0.95.b In repeated samples, the probability that x is within 1.96 /n from is 0.95.c Once you take a specific sample and calculate the value of x, you are 95 percent certain that thevalue you calculated is.d In repeated samples, you are 95 percent certain that the value of x is.8As part of a course assignment to develop an interval estimate for the proportion of IUPUIstudents who smoke tobacco, each of 480 E270 students collects his or her own random sampleof n=400 IUPUI students to construct a 95 percent confidence interval. Considering the 480intervals constructed by the E270 students, we would expect ________ of these intervals tocapture the population proportion of IUPUI students who smoke tobacco.a480b456c400d3809abcdAssume the actual population proportion of IUPUI students who smoke tobacco is 20 percent(0.20). What proportion of sample proportions obtained from random samples of size n=300 arewithin a margin of error of 3 percentage points (0.03) from the population proportion?0.80640.84720.88580.905010To estimate the average number of customers per business day visiting a branch of Fifth NationalBank, in a random sample of n = 9 business days the sample mean number of daily customervisits is x = 250 with a sample standard deviation of s = 36 customers. The 95 percentconfidence interval for the mean daily customer visits is:a (205, 295)b (217, 283)c (222, 278)d (226, 274)11abcdIn the previous question, how large a sample should be selected in order to have a margin of errorof 5 daily customer visits? Use the standard deviation in that question as the planning value.7810113920012Compared to a confidence interval with a 90 percent confidence level, an interval based on thesame sample size with a 99 percent level of confidence:a is wider.b is narrower.c has the same precision.d would be narrower if the sample size is less than 30 and wider if the sample size is at least 30.13It is estimated that 80% of Americans go out to eat at least once per week, with a margin of errorof 0.04 and a 95% confidence level. A 95% confidence interval for the population proportion ofAmericans who go out to eat once per week or more is:a (0.798, 0.802)b (0.784, 0.816)c (0.771, 0.829)d (0.760, 0.840)14In a random sample of 600 registered voters, 45 percent said they vote Republican. The 95%confidence interval for proportion of all registered voters who vote Republican is,a (0.401, 0.499)b (0.410, 0.490)c (0.421, 0.479)d (0.426, 0.474)John is the manager of an election campaign. Johns candidate wants to know what proportion ofthe population will vote for her. The candidate wants to know this with a margin of error of0.01 (at 95% confidence). John thinks that the population proportion of voters who will vote forhis candidate is 0.50 (use this for a planning value). How big of a sample of voters should youtake?a9,604b8,888c5,037d1,4991516abcdIf the candidate changes her mind and now wants a margin-of-error of 0.03 (but still 95% confidence),John could select a different sample of the same size, but adjust the error probability.John should select a larger sample.John should select a smaller sample.John should inform the candidate that margin of error does not impact the sample size.17In a test of hypothesis, which of the following statements about a Type I error and a Type II erroris correct:a Type I: Reject a true alternative hypothesis.Type II: Do not reject a false alternative hypothesis.b Type I: Do not Reject a false null hypothesis. II: Reject a true null hypothesis.Typec Type I: Reject a false null hypothesis.Type II: Reject a true null hypothesis.d Type I: Reject a true null hypothesis.Type II: Do not reject a false null hypothesis.18You are reading a report that contains a hypothesis test you are interested in. The writer of thereport writes that the p-value for the test you are interested in is 0.0831, but does not tell you thevalue of the test statistic. Using as the level of significance, from this information you ______a decide to reject the hypothesis at = 0.10, but not reject at = 0.05.b cannot decide based on this limited information. You need to know the value of the test statistic.c decide not to reject the hypothesis at = 0.10, and not to reject at = 0.05d decide to reject the hypothesis at = 0.10, and reject at = 0.0519Linda works for a charitable organization and she wants to see whether the people who donate toher organization have an average age over 40 years. She obtains a random sample of n = 180donors and the value of the sample mean is x = 42 years, with a sample standard deviation of s =18 years. She wants to conduct the test of H: 40 with a 5% level of significance. Sheshould reject H if the value of the test statistic is _____a less than the critical value.b greater than the critical value.c more than two standard errors above the critical value.d equal to the critical value.20 Now she performs the test and obtains the test statistic of TS = ______,a 1.49 and does not reject H. She concludes that the average age is not over 40.b 1.49 and rejects H. She concludes that the average age is over 40.c 1.74 and does not reject H. She concludes that the average age is not over 40.d 1.74 and rejects H. She concludes that the average age is over 40.21 The probability value for Lindas hypothesis test is ______.a0.0207b0.0409c0.0542d0.0681The Census Bureaus American Housing Survey has reported that 80 percent of families choosetheir house location based on the school district. To perform a test, with a probability of Type Ierror of 5 percent, that the population proportion really equals 0.80, in a sample of 600 families504 said that they chose their house based on the school district. The null hypothesis would berejected if the sample proportion falls outside the margin of error. The margin of error for the testis:a0.039b0.032c0.025d0.0202223 The probability value for the hypothesis test in the previous question is:a0.0026b0.0071c0.0142d0.022424Given the following sample data, is there enough evidence, at the 5 percent significance level, thepopulation mean is greater than 7?x921517811135Compute the relevant test statistic.a The test statistic is 1.683 and the critical value is 1.895. Do not reject the null hypothesis andconclude that the population mean is not greater than 7.b The test statistic is 1.683 and the critical value is 1.895. Reject the null hypothesis and concludethat the population mean is greater than 7.c The test statistic is 2.432 and the critical value is 2.365. Reject the null hypothesis and concludethat the population mean is greater than 7.d The test statistic is 2.432 and the critical value is 1.895. Reject the null hypothesis and concludethat the population mean is not greater than 7.Next SIX questions are based on the following regression modelIn a regression model relating the price of homes (in \$1,000) as the dependent variable to theirsize in square feet, a sample of 20 homes provided the following regression output. Some of thecalculations are left blank for you to compute.SUMMARY OUTPUTRegression StatisticsMultiple R0.7760R SquareAdjusted R Square0.5801Standard ErrorObservations20ANOVARegressionResidualTotaldfSS118 13960.4919 35094.63Coefficients Std ErrorIntercept 15.8479 25.0665Size (Square Feet)0.06950.0133MSF Significance F27.2494 5.78E-05t StatP-value Lower 95% Upper 95%0.6320.5352 -36.81568.5115.79E-050.041625 The model predicts that the price of a home with a size of 2,000 square feet would be ______ thousand.a\$148.70b \$154.80c\$159.50d \$164.3026 The sum of squares regression (SSR) is:a 49055.12b 35094.63c 21134.14d 13960.4927abcdThe regression model estimates that _____% of the variation in the price of the home is explainedby the size of the homes.60.20%65.60%71.50%77.20%28 The standard error of the regression (standard error of estimate) is ______.a30.634b33.698c27.849d24.06729abcd30abcdThe value of the test statistic to test the null hypothesis that property size does not influence theprice of the property is ______.4.3485.2266.3916.982The margin of error to build a 95% confidence interval for the slope coefficient that relates theprice response to each additional square foot is _______.0.0420.0320.0340.028

Paper#61306 | Written in 18-Jul-2015

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