# STATS 38 Multiple Choice Questions 2015

First a confidence interval is constructed without using the finitepopulation correction factor. Then, for the same identical data, a confidenceinterval is constructed using the finite population correction factor. Thewidth of the interval with the finite population correction factor is wider thanthe confidence interval without the finite population correction factor. (Ch9)Question 1.1.(Points : 8)TrueFalseA response bias (measurement error) may occur more in Censusthan in Sample. (Ch9) (Points : 8)Question 2.2.TrueFalseWhen the null hypothesis is not rejected, there is no possibility ofmaking a Type I error. (Ch10) (Points : 8)Question 3.3.TrueFalseQuestion 4.4.If n=20 and p=.4, then the mean of the binomial distribution is 8(Ch6)(Points : 8)TrueFalseThe level of significance indicates the probability of rejecting afalse null hypothesis. (Ch10)Question 5.5.(Points : 8)TrueFalseQuestion 6.6.As the level of significance increases, we are more likely toreject the null hypothesis. (Ch10) (Points : 8)TrueFalseA sample statistic is an unbiased point estimate of a populationparameter if the mean of the populations of all possible values of thesample statistic equals the population parameter. (Ch8)Question 7.7.(Points : 8)TrueFalseIf p=.8 and n=50, then we can conclude that the samplingdistribution of the proportions is approximately a normal distribution.(Ch8) (Points : 8)Question 8.8.TrueFalseFor a binomial probability experiment, with n=150 and p=.2, it isappropriate to use the normal approximation to the binomial distribution.(Ch7)Question 9.9.(Points : 8)TrueFalseIf the level of confidence and sample size remain the same, aconfidence interval for a population proportion p will be narrower when p(1p) is larger than when it is smaller. (Ch9)Question 10.10.(Points : 8)TrueFalseA continuous random variable may assume only integer valuesin a given interval. (Ch7)Question 11.11.(Points : 8)TrueFalseEverything else being constant, increasing the sample sizedecreases the probability of committing a Type II error. (Ch10)Question 12.12.(Points : 8)TrueFalseIf events A and B are mutually exclusive, then P(A and B) isalways equal to zero. (Ch5)Question 13.13.(Points : 8)TrueFalseIf the random variable of x is normally distributed, 68.26% of allpossible observed values of x will be within two standard deviations of themean. (Ch7)Question 14.14.(Points : 8)TrueFalseQuestion 15.15.A Type II error is failing to reject a false null hypothesis.(Ch10) (Points : 8)TrueFalseQuestion 16.16.A standard normal distribution has a mean of _____ andstandard deviation of _____. (Ch7)(Points : 12)Zero, ZeroZero, OneOne, OneOne, ZeroThe set of all possible experimental outcomes is called a(n):(Ch5) (Points : 12)Question 17.17.Sample spaceEventExperimentProbabilityNone of the aboveWhen determining the sample size, if the value found is not aninteger initially, the next highest integer value will ____________ be chosen.(Ch9) (Points : 12)AlwaysQuestion 18.18.SometimesNeverWhich of the following signs would not be used in stating a nullhypothesis? (Ch10)Question 19.19.(Points : 12)=<1 and 2Of all individual tax returns, 37% include errors made by thetaxpayer. If IRS examiners are assigned randomly selected returns inbatches of 12, find the mean and standard deviation for the number oferroneous returns per batch. (Ch6)Question 20.20.(Points : 12)? =2.80, standard deviation =1.67? =4.44, standard deviation =1.67? =4.44, standard deviation =2.80? =7.56, standard deviation =2.80The MPG (Miles per Gallon) for a mid-size car is normallydistributed with a mean of 32 and a standard deviation of .8. What is theprobability that the MPG for a selected mid-size car would be: More than33.2? (Ch7)Question 21.21.(Points : 12)43.32%6.68%93.32%86.64%13.36%Question 22.22.The population of all sample proportions has a normaldistribution if the sample size (n) is sufficiently large. A rule of thumb forensuring that n is sufficiently large is: (Ch8) (Points : 12)np 10n(1p)>= 10np(1-p) 10n(1p) 10 and np 10np 10 and n(1p) 10All of the following are assumptions of the error terms in thesimple linear regression model except (Ch13)Question 23.23.(Points : 12)Errors are normally distributedError terms are dependent on each otherError terms have a mean of zeroError terms have a constant varianceError terms are independent of the Explanatory variableQuestion24.24.(Points : 12)H0 is rejectedH0 is not rejectedH0 may or may not be rejected depending on the sample size nAdditional information is needed and no conclusion can be reachedabout whether H0 should be rejectedA six faced fair die is rolled 36 times. Let X be defined as thenumber of times an even number appears. What is the standard deviationof the variable X? (Ch6)Question 25.25.(Points : 12)189631.732The _______ of two events X and Y is another event that consistsof the sample space outcomes belonging to either event X or event Y orboth event X and Y (Ch5) (Points : 12).ComplementQuestion 26.26.UnionIntersectionMultiplicative probabilityThe width of a confidence interval will be: (Ch9) (Points : 12)Narrower for 99% confidence than for 90% confidenceQuestion 27.27.Wider for a sample size of 64 than for a sample size of 36Wider for a 99% confidence than for 95% confidenceNarrower for sample size of 25 than for a sample size of 36None of the aboveQuestion 28.28.The average customer waiting time at a fast food restauranthas been 7.5 minutes. The customer waiting time has a normal distribution.The manager claims that the use of a new system will decrease averagecustomer waiting time in the store. What is the null and alternativehypothesis for this scenario? (Ch10)(Points : 12)H0: =7.5 and HA: 7.5H0: 7.5 and HA:> 7.5H0: 7.5 and HA:< 7.5H0: <7.5 and HA: 7.5H0: > 7.5 and HA:7.5In the most recent election, 19% of all eligible college studentsvoted. If a random sample of 20 students were surveyed, find theprobability that exactly half (that is 10 out of 20) voted in the election.(Ch6)Question 29.29.(Points : 12)0.00000.00140.01480.4997A multiple-choice test has 30 questions and each one has fivepossible answers, of which one is correct. If all answers were guesses, findthe probability of getting exactly four correct answers. (Ch6)Question 30.30.(Points : 12)0.06040.13250.25520.8000The diameter of small Nerf balls manufactured at a factory inChina is expected to be approximately normally distributed with a mean of5.2 inches and a standard deviation of .08 inches. Suppose a random sampleof 20 balls are selected. What percentage of sample means will be less than5.15 inches? (Ch8)Question 31.31.(Points : 25)A microwave manufacturing company has just switched to anew automated production system. Unfortunately, the new machinery hasbeen frequently failing and requiring repairs and service. The company hasbeen able to provide its customers with a completion time of 6 days or less.To analyze whether the completion time has increased, the productionmanager took a sample of 25 jobs and found that the sample meancompletion time was 6.5 days with a sample standard deviation of 1.5 days.At a significance level of .05, test whether the completion time hasincreased.Question 32.32.(form the hypotheses, show the critical and calculated values of the teststatistic and perform the test) (Ch10)(Points : 25)Question 33.33.Based on a random sample of 25 units of product X, the average weight is104 lbs. and the sample standard deviation is 10 lbs. We would like to decideif there is enough evidence to establish that the average weight for thepopulation of product X is greater than 100 lbs. Assume the population isnormally distributed. What is the critical value (given in terms of the value ofthe test statistic) at=.01? What is the calculated value of the test statistic?form the hypotheses according to the question and perform the test at 1%significance level. (Ch10)(Points : 25)Suppose that the waiting time for a license plate renewal at alocal office of a state motor vehicle department has been found tobe normally distributed with a mean of 30 minutes and a standard deviationof 8 minutes. What is the probability that a randomly selected individual willhave a waiting time between 15 and 45 minutes. (Ch7)Question 34.34.(Points : 25)The probability that an appliance is in repair is .5. If anapartment complex has 100 such appliances, what is the probability that atleast 60 will be in repair? Use the normal approximation to the binomial.Question 35.35.(Ch7)(Points : 25)The College Student Journal (December 1992) investigateddifferences in traditional and nontraditional students, where nontraditionalstudents are defined as 25 years or older and working. Based on the studyresults, we can assume the population mean and standard deviation for theGPA of nontraditional students is µ=3.5 and =0.5. Suppose a randomsample of 100 nontraditional students is selected and each student’s GPA iscalculated. What is the probability that the random sample of 100nontraditional students have a mean GPA greater than 3.65? (Ch8)Question 36.36.(Points : 25)The J.O. Supplies Company buys calculators from a Koreansupplier. The probability of a defective calculator is 10%. If 100 calculatorsare selected at random, what is the standard deviation of the number ofdefectives? (Ch6)Question 37.37.(Points : 25)A local tire dealer wants to predict the number of tires sold eachmonth. He believes that the number of tires sold is a linear function of theamount of money invested in advertising. He randomly selects 6 months ofdata consisting of tire sales (in thousands of tires) and advertisingQuestion 38.38.expenditures (in thousands of dollars). Based on the data set with 6observations, the simple linear regression model yielded the followingresults.X =24X2=124Y = 42Y2 =338XY =196Calculate the coefficient of determination and the coefficient of correlationbetween X and Y Interpret the coefficient of Determination. also find the slope and intercept and write the estimated Regression equation. Whatwould the predicted sales of tires be if he spends five thousand dollars inadvertising? (Ch13)(Points : 25)

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