Inference
Which of the following is a true statement?
A.) Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis
B.) A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false
A.)
We attempt to show that the null hypothesis is unacceptable by showing that it is improbable; however, we can't show that it is definitely true or false. If there is interest in deviation in only one direction, the alternative hypothesis is expressed using either < or >.
How many teeth does an aardvark have?
None
On a windless day, a member of a high school's football team, its punting specialist, kicks two identical footballs, one filled with helium, and one filled with air, ten times each. He alternates footballs and is not told there is any difference. The distances (in yards) of the kicks are recorded in the table below.
Helium:36, 40, 37, 34, 35, 35, 42, 36, 31, 36
Air :38, 37, 31, 36, 40, 34, 37, 36, 34, 34
Assuming that all assumptions for inference are met, which test should be used to determine if there is a statistical difference in yards kicked using the two balls?
A.) A two-sample t-test
B.) A two-sample z-test
A
The data are not paired (as they would be if there were ten punters each taking one kick with each ball). We are comparing population means, with unknown population standard deviations, so a t-test is the proper procedure.
A.) y=-6+2x
B.) y=6-x
B
What is the probability of a type 2 error when a hypothesis test is being conducted at the 5% significance level?
A.) .95
B.) There is insufficient information to answer this question
B
There is a different probability of Type 2 error for each possible correct value of the population parameter.
A geneticist claims that four species of fruit flies should appear in the ration 1:3:3:9. Suppose that a sample of 480 flies contained 25, 92, 68, and 295 flies of each species, respectively. Does a chi-square test show sufficient evidence to reject the geneticist's claim?
A.) The test DOES NOT give sufficient evidence to reject the geneticist's claim.
B.) The test DOES gives sufficient evidence to reject the geneticist's claim.
B.)
Since 1+3+3+9=16 according to the geneticist the expected number of fruit flies of each species is 1/16(480)=30, 3/16(480)=90, 3/16(480)=90, and 9/16(480)=270. we calculate:
x2=(25-30)2/30 +(92-90)2/90+(68-90)2/90+(295-270)2/270=8.570
with a P-value of .0356 there is sufficient evidence to reject the geneticist's claim
Which ancestor of the calculator came first, The abacus or the slide rule?
The Abacus
There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw between 45% and 55% heads. In the second game, you win if you can throw more than 60% heads. For each game would you rather flip the coin 20 times or 40 times?
A.) 20 times for the first game and 40 times for the second
B.) 40 times for the first game and 20 times for the second
B
The probability of throwing heads is .5. By the law of large numbers, the more the relative frequency tends to become closer to this probability. With fewer tosses (a smaller sample size), there is more chance for wide swings in the relative frequency.
A doctor wishes to compare the resting heart rates of his younger patients (younger than 30 years old) versus his older patients (older than 30 years old). Which of the following graphical displays in inappropriate?
A.) Scatterplot
B.) Side-by-side histograms
A
A scatterplot is used to study a relationship between two quantitative variables.
A fitness center advertises that the average pulse rate of its members is 68.4 bpm. A high school AP Statistics instructor suspects this is a made-up number and runs a hypothesis test on an SRS of 48 members, calculating a mean of 71.0bpm with a standard deviation of 10.3 bpm. In which of the following intervals is the P-value located?
A.) P>.10
B.) .05<P<.10
B
The standard deviation of the sample means is 1.487. The t-score for 71.0 is 1.748
Two confidence interval estimates from the same sample are (72.2, 77.8) and (71.3, 78.7). One estimate is at the 95 percent level, and the other is at the 99 percent level. Which is which?
A.) (72.2, 77.8) is the 99 percent levelB
The narrower interval corresponds to the lower confidence level (77.8-72.2=5.6 is less than 78.7-71.3=7.4)
The first hockey pucks used in early outdoor hockey games were made of what?
Frozen Cow Dung
Is the waiting time (in minutes) between eruptions of Old Faithful lengthening? Random samples of waiting times were noted from two consecutive years with the summary statistics:
Average waiting time Year 1: 85 Year 2: 87.5
Standard of deviation Year 1: 8 Year 2: 8
Number of eruptions Year 1: 45 Year 2: 39
Is there statistical evidence that Old Faithful is slowing down (not as faithful)?
A.) No, because the P-value is greater than.10
B.) Yes, .05<P<.10, indicating some evidence of a slowdown.
B
A one-sided, two-sample t-test gives t=-1.428 and p=.0785
if quartiles Q1=50 and Q3=70, which of the following must be true?
A.) The median is 60
B.) the mean is between 50 and 70
C.) none may be true
C
The median is somewhere between 50 and 70, but not necessarily 60. Even a single very large score can result in a mean over 70 and a standard deviation over 20.
A guidance counselor wishes to determine the mean number of changes in asademic major by college students to within +/- .1 at a 90% confidence level. What sample size should be chosen if it is known that the standard deviation is .45?
A.) 55
B.) 110
A
To test whether husbands or wives have greater manual agility, an SRS of 50 married couples a=is chosen, and all 100 people are given a 1-minute period to find and place strangely shaped pegs into matching holes. what is the conclusion at a 5% significance level if a two-sample hypothesis test results in a P-value of .15?
A.) The observed difference is not significantB
The two-sample hypothesis test should be used only when the two sets are independent. In this case, there is a clear relationship between the data, in pairs, and this relationship is completely lost in the procedure for the two-sample test. The proper procedure is to run a one-sample test on the single variable consisting of the differences from the paired data.
Who sang about being an “eggman” and a “walrus”?
The Beatles
Can dress size be predicted from a woman's height? in a random sample of 20 female high school students, dress size versus height (cm) gives the following regression results:
Predictor Coef CoefSE T P
Constant -48.81 30.57 -1.6 .128
Height .3736 .1898 1.97 .065
S=4.4672 R-Sq=17.7% R-Sq(adj)=13.1%
A.) For every 1cm increase in height, there is a predicted increase of .3736 in dress size on average
B.) .3736 is a measure of the variability in heights
A
.3736 is the slope of the regression line, and height is the independent variable.
Which of the following statements about the correlation coefficient r is incorrect?
A.) It is not affected by changes in the measurement units of the variables.
B.) it is not affected by extreme values.
C.) It is not affected by which variable is called x and which is called y.
B
In a one-sided hypothesis test for the mean, for a random sample size 15 the t-score of the sample mean is 2.615. Is this significant at the 5% level? At the 1% level?
A.) Significant at the 1 % level but not at the 5% level
B.) Significant at the 5% level but not at the 1% level
B
A college recruiter is interested in comparing the SAT math and verbal scores of applicants to the college. An SRS of 40 applicants is chosen, and the math and verbal scores are noted. Which of the following is a proper test?
A.) One sample test on differences of paired data
B.) Chi-square goodness-of-fit test
A
Two-sample tests require that the two samples being compared be independent of each other. However, in this case, the data occur in related pairs, namely the SAT math and SAT verbal scores of each individual applicant. The proper procedure is to run a one-sample test on the single variable consisting of the difference between math and verbal SAT scores for each applicant.
What was Marilyn Monroe’s natural hair color?
Red
A guidance counselor hands out a questionnaire about drug use to students whom she feel represent a cross section of the high school population, and asks the students to deposit the completed questionnaire in a box near the building front door at the end of the day. Which of the following is not a valid concern?
A.)Judgment sample bias (quota sampling)
B.) Voluntary response bias
C.) None of the above
D.) All of the above
D.
Even experts overlook features of a population, students who are interested in an issue are more likely to respond, and students might be tempted to lie rather than to admit to an illegal activity.
When there are multiple gaps and clusters, which of the following is the best choice to give an overall picture of a distribution?
A.) Stemplot or histogram
B.) Mean and standard deviation
C.) Boxplot with its five-number summary
A
Stemplots and histograms can show gaps and clusters that are hidden when one simply looks at calculations such as mean median, standard deviation, quartiles, and extremes
A confidence interval estimate is determined from the summer earnings of an SRS of n students. All other things being equal, which of the following will result in a smaller margin of error?
A.) Introducing bias into sampling
B.) A larger sample size
B
The margin of error varies directly with the critical z-value and directly with the standard deviation of the sample, but inversely with the square root of the sample.