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##### 20 MCQ Statistics and Probability

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Question;Manufacturers use random samples to test whether or not their product is meeting specifications. These samples could be people, manufactured parts, or even samples during the manufacturing of potato chips.Do you think that all random samples taken from the same population will lead to the same result?A) YesB) NoC) Not enough dataD) None of the above2.Manufacturers use random samples to test whether or not their product is meeting specifications. These samples could be people, manufactured parts, or even samples during the manufacturing of potato chips.What characteristic (or property of random samples) could be observed during the sampling process?A) VariabilityB) ExactnessC) RandomnessD) None of the above3.A certain population has a mean of 500 and a standard deviation of 30. Many samples of size 36 are randomly selected and the means calculated.What value would you expect to find for the mean of all these sample means?A) 36B) 500C) 500/36D) None of the above4.The number of engines owned per fire department was obtained from a random sample taken from the profiles of fire departments from across the United States. The results are as follows:29 8 7 33 21 26 6 11 4 54 7 4Use the point data to find a point estimate for the standard deviation.A) Approximately 25.5B) Approximately 15.5C) Approximately 10.5D) Approximately 5.55.State the null hypothesis H0 and the alternative hypothesis Ha that would be used to test the following claim:A chicken farmer at Best Broilers claims that the chickens have a mean weight of 56 ounces.A) H0 =? = 56 vs Ha:?? 56B) H0 =?? 56 vs Ha:? = 56C) H0 =? = 56 vs Ha:? = 56D) None of the above6.The students at a local high school were assigned to do a project for their statistics class. The project involved having sophomores take a timed test on geometric concepts. The statistics students would then use these data to determine whether there was a difference between male and female performances. Would the resulting sets of data represent dependent or independent samples?A) Dependent. The samples are taken from the same set of students.B) Dependent. The samples are from two separate and different sets of students.C) Independent. The two samples are from two separate and different sets of students.D) Independent. The samples are taken from the same set of students.7.Experts have estimated that 25% of all homeless people in the U.S. are veterans. The proportion of Americans in general who are homes is 0.11. For random samples of 100 people, which is more normal?A) Distribution of sample proportion, when the population proportion is 0.11B) Distribution of sample proportion, when the population proportion is 0.25C) Both are the sameD) None of the above8.Many biologists and anthropologist claim that 10 percent of all children conceived in the context of a marriage have been fathered by someone from outside the couple.In this situation, the standard deviation from samples of 225 births is 0.02. If the sample size were decreased, the standard deviation would beA) SmallerB) LargerC) The sameD) There is not enough information9.The probability of birth by Caesarean in the U.S. is 0.30If the probability of Caesarean birth is 0.30, and 140 in a sample of 500 births are Caesarean, which of these numbers is n?A) 0.30B) 140C) 500D) 140/50010.This graph shows the distribution of ACT scores for a population of students.Which of these is your best guess for the probability of a score being greater than 30?A) 0.016B) 0.036C) 0.16D) 0.3611.Online interviews of 1500 parents with children under the age of eight found the proportion who read to their children at least 20 minutes a day to be 0.78. Suppose a reporter would like to claim that more than three-fourths (0.75) of all parents with children under eight read to them at least twenty minutes daily.What notation is used for the number 0.75?A) pB) p?C) p0D) None of the above12.A Type I Error is rejecting the null hypothesis, even though it is true, a Type II Error is failing to reject the null hypothesis, even though it is false.Merck developed an AIDS vaccine that showed promise in initial tests. Unfortunately, in a subsequent test conducted internationally on a large group of volunteers, those vaccinated were no less likely to become infected than those who were not vaccinated. Apparently, Merck?s conclusion in the initial tests wasA) a Type I ErrorB) a Type II ErrorC) both (a) and (b)D) neither (a) nor (b)13.Each student in a class of 80 rolls 8 dice in order t perform inference about the mean of all dice rolls (which happens to be 3.5).Suppose each student uses his or her sample to test the true null hypothesis that the population mean is 3.5 against the two-sided alternative. About how many of these 80 tests should reject at the?=0.05 level?A) 0B) 4C) 8D) 28E) 5214.Students compared tuition, in thousands of dollars, for samples of public and private colleges/universities in the US.N Mean St. Dev SEMeanPublic 5 7.26 1.48 0.66Private 6 32.32 3.30 1.3Difference =? public -? privateEstimate for differences: -25.06T-Test of difference =0 (vs. not =): T-Value = XXXX P-Value = 0.000 DF=7A) Paired studyB) Two-sample studyC) Both of the aboveD) None of the above15.A sleep-lab study found that a group of subjects with a mean age of about 68 years slept significantly less than the group of subjects with a mean age of 22 years, with the former averaging only 7.4 hours and the latter 8.9 hours. In contrast, an ANOVA procedure on student survey data found no significant difference in hours slept among 1st, 2nd, 3rd, and 4th year students. In general, to produce evidence of a relationship between sleep and age, which is more helpful?A) include individuals who are all roughly the same ageB) include individuals spanning a wide range of agesC) it doesn?t matter how similar or different the ages are16.ANOVA was used to compare samples of weekly hotel rates at three Mexican resorts: Cancun, Puerto Vallarta, and Los Cabos.Which of these best describes the relative rates?A) one of the resorts was much cheaper than the other twoB) one of the resorts was much more expensive than the other twoC) all three resorts? rates were quite similar17.What does the null hypothesis state?A) x?1 = x?2 = x?3B)?1 =?2 =?318.What does the alternative hypothesis state?A) All three population means are differentB) Not all of the population means are differentC) Not all three population means are the same19.You are a researcher, and have set up a hypothesis test of?. You want to compare the value of the sample mean to the value of the population mean as stated in the null hypothesis. This comparison is accomplished using the test statistic:A) Z-testB) F-testC) Chi-square20.When would you use a t-statistic vs. a z-statistic?A) when the standard deviation is known and the sample population is normally distributedB) when the sample population is normally distributedC) Both a & bD) None of the above

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