# The sampling distribution of x? is approximately normal if

1The right way to think about the sample mean is:aThe sample mean is a constant number.bThe sample mean is a different value in each random sample from the population mean.cThe sample mean is always close to the population mean.dThe sample mean is always smaller than the population mean.2The sampling distribution of x? is approximately normal if a. the distribution of x is skewed.bthe distribution of x is approximately symmetriccthe sample size is large enough.dthe sample size is small enough.3There 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 (without replacement). The total number of possible sample is _____.a6b12c18d204The mean daily output of an automobile manufacturing plant is ? = 520 cars with standard deviation of ? = 14 cars. In a random sample of n = 49 days the probability that the sample mean output of cars (x?) will be within ±3 cars from the population mean is _________.a0.9876b0.9544c0.9266d0.86645In the population of IUPUI undergraduate students 38 percent (0.38) enroll in classes during the summer sessions. Let p? denote the sample proportion of students who plan to enroll in summer classes in samples of size n = 200 selected from this population. The expected value of the sample proportion E(p?) is _______.a0.38b0.28c0.25d0.186In the previous question the standard error of the sampling distribution of p? is se(p?)=_______.a0.0343b0.0297c0.0248d0.02217The expression.png”>Means:aOnce you take a specific sample and calculate the value of x? the probability that the value of x? you just calculated is within ±1.96 ?/?n from ? is 0.95.bIn repeated samples the probability that x? is within ±1.96 ?/?n from ? is 0.95.cOnce you take a specific sample and calculate the value of x? you are 95 percent certain that the value you calculated is ?.dIn 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 IUPUI students who smoke tobacco each of 480 E270 students collects his or her own random sample of n=400 IUPUI students to construct a 95 percent confidence interval. Considering the 480 intervals constructed by the E270 students we would expect ________ of these intervals to capture the population proportion of IUPUI students who smoke tobacco.a480b456c400d3809Assume 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 are within a margin of error of ±3 percentage points (±0.03) from the population proportion?a0.8064b0.8472c0.8858d0.905010To estimate the average number of customers per business day visiting a branch of Fifth National Bank in a random sample of n = 9 business days the sample mean number of daily customer visits is x? = 250 with a sample standard deviation of s = 36 customers. The 95 percent confidence interval for the mean daily customer visits is:a(205 295)b(217 283)c(222 278)d(226 274)11In the previous question how large a sample should be selected in order to have a margin of error of ±5 daily customer visits? Use the standard deviation in that question as the planning value.a78b101c139d20012Compared to a confidence interval with a 90 percent confidence level an interval based on the same sample size with a 99 percent level of confidence:ais wider.bis narrower.chas the same precision.dwould 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 error of 0.04 and a 95% confidence level. A 95% confidence interval for the population proportion of Americans 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)15John is the manager of an election campaign. John’s candidate wants to know what proportion of the population will vote for her. The candidate wants to know this with a margin of error of ± 0.01 (at 95% confidence). John thinks that the population proportion of voters who will vote for his candidate is 0.50 (use this for a planning value). How big of a sample of voters should you take?a9 604b8 888c5 037d1 49916If the candidate changes her mind and now wants a margin-of-error of ± 0.03 (but still 95% confidence) aJohn could select a different sample of the same size but adjust the error probability.bJohn should select a larger sample.cJohn should select a smaller sample.dJohn 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 error is correct:aType I: Reject a true alternative hypothesis.Type II: Do not reject a false alternative hypothesis.bType I: Do not Reject a false null hypothesis.Type II: Reject a true null hypothesis.cType I: Reject a false null hypothesis.Type II: Reject a true null hypothesis.dType 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 the report writes that the p-value for the test you are interested in is 0.0831 but does not tell you the value of the test statistic. Using ? as the level of significance from this information you ______adecide to reject the hypothesis at ? = 0.10 but not reject at ? = 0.05.bcannot decide based on this limited information. You need to know the value of the test statistic.cdecide not to reject the hypothesis at ? = 0.10 and not to reject at ? = 0.05ddecide 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 to her organization have an average age over 40 years. She obtains a random sample of n = 180 donors 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. She should reject H? if the value of the test statistic is _____aless than the critical value.bgreater than the critical value.cmore than two standard errors above the critical value.dequal to the critical value.20Now she performs the test and obtains the test statistic of TS = ______ a1.49 and does not reject H?. She concludes that the average age is not over 40.b1.49 and rejects H?. She concludes that the average age is over 40.c1.74 and does not reject H?. She concludes that the average age is not over 40.d1.74 and rejects H?. She concludes that the average age is over 40.21The probability value for Linda’s hypothesis test is ______.a0.0207b0.0409c0.0542d0.068122The Census Bureau’s American Housing Survey has reported that 80 percent of families choose their house location based on the school district. To perform a test with a probability of Type I error of 5 percent that the population proportion really equals 0.80 in a sample of 600 families 504 said that they chose their house based on the school district. The null hypothesis would be rejected if the sample proportion falls outside the margin of error. The margin of error for the test is:a0.039b0.032c0.025d0.02023The 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 the population mean is greater than 7?x921517811135Compute the relevant test statistic.aThe test statistic is 1.683 and the critical value is 1.895. Do not reject the null hypothesis and conclude that the population mean is not greater than 7.bThe test statistic is 1.683 and the critical value is 1.895. Reject the null hypothesis and conclude that the population mean is greater than 7.cThe test statistic is 2.432 and the critical value is 2.365. Reject the null hypothesis and conclude that the population mean is greater than 7.dThe test statistic is 2.432 and the critical value is 1.895. Reject the null hypothesis and conclude that 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 their size in square feet a sample of 20 homes provided the following regression output. Some of the calculations are left blank for you to compute.SUMMARY OUTPUTRegression StatisticsMultiple R0.7760R SquareAdjusted R Square0.5801Standard ErrorObservations20ANOVAdfSSMSFSignificance FRegression127.249375.78E-05Residual1813960.49Total1935094.63CoefficientsStd Errort StatP-valueLower 95%Upper 95%Intercept15.847925.06650.6320.5352-36.81568.511Size (Square Feet)0.06950.01335.79E-050.041625The 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$164.3026The sum of squares regression (SSR) is:a49055.12b35094.63c21134.14d13960.4927The regression model estimates that _____% of the variation in the price of the home is explained by the size of the homes.a60.20?5.60?1.50?7.20(The standard error of the regression (standard error of estimate) is ______.a30.634b33.698c27.849d24.06729The value of the test statistic to test the null hypothesis that property size does not influence the price of the property is ______.a4.348b5.226c6.391d6.98230The margin of error to build a 95% confidence interval for the slope coefficient that relates the price response to each additional square foot is _______.a0.042b0.032c0.034d0.028

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