Statistical Methods and Hypothesis Testing: Practice Questions and Solutions

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Statistical Methods and Hypothesis Testing: Practice Questions andSolutions1.In a statistical study thepopulationisA)the group of people from which the sample is takenB)all of the people in the United StatesC)all of the people inthe worldD)the people who comprise the sampleFeedback:The population is the larger group of people from which the sample was takenPoints Earned:0.0/1.0Correct Answer(s):A2.The sample mean is an estimate of:A)The average value forpeople NOT in the populationB)The average value in the sampleC)The true population meanFeedback:The sample mean is anestimateof the true population mean. It is, however,anexactmeasurement of the average value in the sample since thesample data is what is used tocalculate the sample mean.Points Earned:0.0/1.0Correct Answer(s):C3.A summary measure calculated from the sample is called a(n):A)parameterB)statisticC)outlierFeedback:Sample measures arestatistics; population measures are parametersPoints Earned:1.0/1.0Correct Answer(s):B

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4.Which of the following is a parameter?A)muB)x-barC)p-hatD)ZFeedback:x-bar and p-hat are sample statistics while Z is a teststatistic.Points Earned:0.0/1.0Correct Answer(s):A5.Which of the following is an example of paired data?A)The average time to cook the same meal is compared for men and women.B)The proportion of children that get a cold in Winter in Pittsburgh is compared to the proportion ofchildren that get a colding in Winter in Dallas.C)A researcher wants to test the time it takes to send a text message for adults and children.D)Data measured to compare handwriting between the left and right hands of 30 subjects.Feedback:Handwriting between left and right hands is paired data since it is repeated measurements onthe same subject.Points Earned:0.0/1.0Correct Answer(s):D6.In a poll of n = 100 randomly selected individuals, 25 people said they are opposed to the death penaltyfor persons convicted of murder. Which expression above correctly shows the calculation of thestandarddeviationof the sample proportion?A)Expression AB)Expression B

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C)Expression CFeedback:The standard error is found by taking the square root of (0.25)*(0.75)/100 = 0.0433Points Earned:1.0/1.0Correct Answer(s):A7.From a random sample of 20 women from a women’s only healthclub, 60%, or 12, stated that theywished the club would stay open longer. Which of the followingbestdefines what this 60% represents?A)populationB)statisticC)parameterD)sampleFeedback:Because this value came from a sample the 60% defines a statistic.Points Earned:0.0/1.0Correct Answer(s):B8.Suppose that 200 different polling organizations and academic researchers all do surveys in which thesame question is asked. All 200 research groups construct a 90% confidenceinterval for the proportionwho would say "yes" to this question. About how many of the 200 different 90% confidence intervals willcapture the value of the population proportion?A)90B)95C)180D)190Feedback:Simply, you would expect to be"correct" 90 percent of the time. So 90 percent of 200 is 180.Points Earned:1.0/1.0Correct Answer(s):C9.

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In a poll of n = 200 randomly selected individuals, 50 people said they are opposed to the death penaltyfor persons convicted ofmurder. Which choice from the display above correctly shows the calculation fora90%confidence interval for the population proportion opposed to the death penalty?A)Equation AB)Equation BC)Equation CD)Equation DFeedback:With a sampleproportion of 50 out or 200 or 0.25 the correct equation would be 0.25 ± thesquare root of [(0.25)*(1−0.25) divided by 200].Points Earned:1.0/1.0Correct Answer(s):D10.Based on the output above, what is the Standard Error of the mean?A)1.60B)2.4C)12.0D)23.8Feedback:The standard error of the mean is found by taking the sample standard deviation, 60, anddividing by the square root of the sample size, which is 5. This results in a standard error of 12.0Points Earned:1.0/1.0Correct Answer(s):C

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11.Suppose a 95% confidence interval for the proportion of Americans who exercise regularly is 0.29 to 0.37.Which one of the following statements isNOTtrue?A)It is reasonable to say that more than 25% of Americansexercise regularly.B)It is reasonable to say that more than 40% of Americans exercise regularly.C)An "acceptable" hypothesis is that about 33% of Americans exercise regularly.D)It is reasonable to say that fewer than 40% of Americans exercise regularly.Feedback:All are reasonable except to say that more than 40% of Americans exercise regularly. This isbecause the confidence interval is less than 40%.Points Earned:1.0/1.0Correct Answer(s):B12.For which of the followingsituations would the Central Limit Theorem for sample meansNOTapply?A)A random sample of size 20 is drawn from a skewed population.B)A random sample of size 50 is drawn from a skewed population.C)A random sample of size 20 is drawn from anormal population.D)A random sample of size 50 is drawn from a normal population.Feedback:For sample sizes of 30 or more the Central Limit Theorem states that even for a skewedpopulation the sample mean distribution will approximated a normal distribution, and if the population isbell-shaped then so to will the distribution of the sample means regardless of sample size. Thus theresponse that does not follow the Rules is the one of sample size of 20 from a skewed distributionPoints Earned:1.0/1.0Correct Answer(s):A13.A 95% confidence interval for the proportion of women that has ever dozed off while driving is 0.07 to0.14. For men, a 95% confidence interval for the proportion that has ever dozed off while driving is 0.19 to0.25.Assume both intervals were computed using large random samples. What conclusion can be madeabout the population proportions that have dozed off while driving?A)Itisreasonable to conclude that there is a difference between men and women.B)It isnotreasonable to conclude that there is a difference between men and women.C)Itisreasonable to conclude that there is a difference of .05 between men and women.D)No conclusion is possible because we don’t know the margin of error.Feedback:Theintervals do not overlap indicating that a statistically significant difference exists.Points Earned:1.0/1.0

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