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##### 30 STATS Multiple Choice Questions

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Question;1;The 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.;2;The sampling;distribution of x? is approximately normal if;a;the distribution of x;is skewed.;b;the distribution of x;is approximately symmetric;c;the sample size is large enough.;d;the sample size is;small enough.;3;There 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 _____.;a;6;b;12;c;18;d;20;4;The 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 _________.;a;0.9876;b;0.9544;c;0.9266;d;0.8664;5;In 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 _______.;a;0.38;b;0.28;c;0.25;d;0.18;6;In the previous;question, the standard error of the sampling distribution of p? is;se(p?)=_______.;a;0.0343;b;0.0297;c;0.0248;d;0.0221;7;The expression;Means;a;Once 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.;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 the value you calculated is?.;d;In repeated samples;you are 95 percent certain that the value of x? is?.;8;As 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.;a;480;b;456;c;400;d;380;9;Assume 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?;a;0.8064;b;0.8472;c;0.8858;d;0.9050;10;To 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);11;In 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.;a;78;b;101;c;139;d;200;12;Compared 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;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.;13;It 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);14;In 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);15;John 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?;a;9,604;b;8,888;c;5,037;d;1,499;16;If the candidate;changes her mind and now wants a margin-of-error of ? 0.03 (but still 95%;confidence);a;John could select a;different sample of the same size, but adjust the error probability.;b;John should select a;larger sample.;c;John should select a smaller sample.;d;John should inform the;candidate that margin of error does not impact the sample size.;17;In a test of;hypothesis, which of the following statements about a Type I error and a Type;II error is 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.;Type II: Reject a true;null hypothesis.;c;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.;18;You 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;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? = 0.05;d;decide to reject the;hypothesis at? = 0.10, and reject at? = 0.05;19;Linda 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;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 Linda?s hypothesis test is ______.;a;0.0207;b;0.0409;c;0.0542;d;0.0681;22;The 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;a;0.039;b;0.032;c;0.025;d;0.020;23;The probability value;for the hypothesis test in the previous question is;a;0.0026;b;0.0071;c;0.0142;d;0.0224;24;Given the following;sample data, is there enough evidence, at the 5 percent significance level;the population mean is greater than 7?;x;9;2;15;17;8;11;13;5;Compute the relevant test;statistic.;a;The 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.;b;The 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.;c;The 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.;d;The 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 model;In 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 OUTPUT;Regression Statistics;Multiple R;0.7760;R Square;Adjusted R Square;0.5801;Standard Error;Observations;20;ANOVA;df;SS;MS;F;Significance F;Regression;1;27.24937;5.78E-05;Residual;18;13960.49;Total;19;35094.63;Coefficients;Std Error;t Stat;P-value;Lower 95%;Upper 95%;Intercept;15.8479;25.0665;0.632;0.5352;-36.815;68.511;Size (Square Feet);0.0695;0.0133;5.79E-05;0.0416;25;The model predicts;that the price of a home with a size of 2,000 square feet would be;thousand.;a;$148.70;b;$154.80;c;$159.50;d;$164.30;26;The sum of squares;regression (SSR) is;a;49055.12;b;35094.63;c;21134.14;d;13960.49;27;The regression model;estimates that _____% of the variation in the price of the home is explained;by the size of the homes.;a;60.20%;b;65.60%;c;71.50%;d;77.20%;28;The standard error of;the regression (standard error of estimate) is ______.;a;30.634;b;33.698;c;27.849;d;24.067;29;The value of the test;statistic to test the null hypothesis that property size does not influence;the price of the property is ______.;a;4.348;b;5.226;c;6.391;d;6.982;30;The margin of error to;build a 95% confidence interval for the slope coefficient that relates the;price response to each additional square foot is _______.;a;0.042;b;0.032;c;0.034;d;0.028

Paper#53090 | Written in 18-Jul-2015

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