STAT3011 Multiple Choice

The p-value for a hypothesis test is (A) the probability that the null hypothesis is true. (B) the probability that the null hypothesis is true, given the value of the test statistic we actually observed. (C) the probability of observing a test statistic at that value or more extreme given the null hypothesis is true (D) All of the above are false.

(C)

The sample mean ̄x is called a ___ of the population mean μ. (A) margin of error (B) confidence level (C) point estimate (D) interval estimate

(C)

A STAT 3011 student flipped a coin multiple times and found the sample proportion of heads to be ˆp= 0.40. Which of the following is a valid confidence interval based on this test statistic for the true proportion? (No calculation necessary) (A) (0.30, 0.50) (B) (0.35, 0.55) (C) (0.40, 0.60) (D) (0.45, 0.65)

(A)

A student in STAT 3011 is interested in the academic performance differences between individuals who wake up before 7AM every morning versus those who do not. If the student finds a significant difference, when in fact one does not exists in the population (A) a Type I error has been made. (B) the null hypothesis was correctly accepted. (C) a Type II error has been made. (D) the alternative hypothesis was correctly accepted.

(A)

Let ̄x denote the sample mean from a sample of size n= 100 from a population distribution with mean 0 and standard deviation 10. Which of the following is TRUE regarding the sampling distribution of ̄x? (A) ̄x has standard deviation 10. (B) ̄x approximately follows a standard normal distribution. (C) ̄x approximately follows at-distribution. (D) None of the above.

(B)

Roll two dice. What is the most likely sum? (A) 6 (B) 7 (C) 9 (D) 11

(B)

Which of the following is not a correct probability statement? (A) P(A∪B) =P(A) +P(B) when A and B are independent (B) P(Sample Space) = 1 (C) P(A) =P(A∩B) +P(A∩Bc) (D) P(Ac) = 1−P(A)

(A)

Which of the following results in a small standard error of the mean? (A) A larger sample size (B) A larger population mean (C) A larger population standard deviation (D) None of the above.

(A)

Which of the following scenario satisfies assumptions for an independent two sample t-test? (A) A random sample of home runs hit by 60 players in the American League and 60 players in the National League. (B) A sample of 15 volunteers' systolic blood pressures before and after taking medication. (C) A random sample of heads from coin flips of a quarter and a penny with 15 successes and 15 failures in each group. (D) A random sample of family sizes of families from Minnesota and Wisconsin, the sample size from each group was 4, and the data do not appear normal.

(A)

If x1, x2,...,xn is a random sample from N(μ,σ), then what is the distribution of the ̄x? (A) ̄x∼N(μ,σ/n) (B) ̄x∼N(μ,σ) (C) ̄x∼N(μ,σ/√n) (D) None of the above.

(C)

In a survey of 1300 American high school students, 32% of the respondents reported that someone had bullied them in school. Which term best describes the value 32%? (A) Population (B) Parameter (C) Statistic (D) Sample

(C)

In a two-sided hypothesis with Ha: μ > μ0 with 30 observations, p-value is found to be 0.02. Which of the following R commands produce the value(s) of test statistic. (A)qt(0.01, df=29), qt(0.99, df=29) (B)1-pt(0.02, df=29) (C)qt(.98, df=29) (D)qt(0.02,df=29)

(C)

Let U be a normal random variable with mean 30 and standard deviation 5. Use the XX-XX-XX.X rule to calculate the probability that 15 < U < 20. (A) 0.135 (B) 0.1585 (C) 0.0235 (D) 0.047

(C)

Suppose that P(A) = 0.4, P(B) = 0.3 and P((A∪B)c) = 0.42. Which one of the following is correct? (A)P(A∩B) = 0.58 (B)A and B are disjoint (C)A and B are independent (D) None of the above

(C)

Suppose x1,x2,...,x100, a sample of size 100 from a population with mean μ= 5 and standard deviation σ= 50, which of the following statements about the distribution of ̄X, the sample mean, is correct? (A) ̄X∼N(5,5) approximately if and only if the population distribution is normal. (B) ̄X∼N(5,0.5) approximately if and only if the population distribution is normal. (C) ̄X∼N(5,5)approximately even if the distribution of the population is highly right skewed. (D) ̄X∼N(5,0.5) approximately even if the distribution of the population is highly rightskewed.

(C)

The distribution of adult male weights is bell-shaped with mean 80 kilograms.If approximately 95% of the weights are between 70 kilograms and 90 kilograms, what is the variance of this distribution? (A) 5 kilograms (B) 10 kilograms2 (C) 25 kilograms2 (D) 40 kilograms2

(C)

Which of the following distributions can take on negative values? (A)normal distribution (B)F-distribution (C)χ2-distribution (D) none of the above

(A)

What is the correct interpretation of the significance level α in a hypothesis test? (A) The probability of rejecting H0 given that H0 is true (B) The probability of NOT rejecting H0 given that Ha is true (C) The probability that H0 is true given that H0 is rejected (D) The probability that Ha is true given that H0 is NOT rejected

(A)

A study considered a drug (a pill called Sumatriptan) for treating migraine headaches in a random sample of 60 subjects. The study observed each subject two times when he or she had a migraine headache. The subject received the drug at one time and a placebo at the other time. The order of the treatment was randomized. For each subject, the response was whether the drug or the placebo provided better pain relief. Which of the following is the correct set of hypotheses in testing whether the pill has any effect? (A) H0: p = 0.5 vs Ha: p6 = 0.5 (B) H0: ˆp = 0.5 vs Ha: ˆp6 = 0.5 (C) H0: ˆp1 = ˆp2 vs Ha: ˆp16 = ˆp2 (D) H0: p1 = p2 vs Ha: p1 ≠ p2

(A)

An educational researcher wanted to know if in-class activities significantly improved students' learning compared to traditional lecture only teaching methods. Ten students matched on GPA, Year in school, and academic major were randomly selected from the current UNM student population. One student from each pair was randomly assigned to either the Lecture Only class or Lecture plus Group Activities class. At the end of the semester, students final exam scores were recorded and teaching methods were compared. Which hypothesis test should the researcher use? (A)***Matched-pair t-test for mean difference (B) One sample z-test for population proportion (C) Independent two-sample z-test for comparing population proportions (D) Independent two-sample t-test for comparing population means

(A)

At a high school with 200 students, 32 play soccer, 18 play basketball, and 8 play both sports. If a student is selected at a random, find the probability that a student plays{neither soccer nor basketball.} (A) 79/100 = 0.79 (B) 1/4 = 0.25 (C) 21/25 = 0.84 (D) 4/5 = 0.8

(A)

Below is R output of a hypothesis test. Select the most appropriate p-value(hidden as XXXXXXX in R output). One Sample t-test data: x t = -2.4295, df = 29, p-value = XXXXXXX alternative hypothesis: true mean is not equal to 2 95 percent confidence interval: 1.079621 1.920969 sample estimates: mean of x 1.500295 (A) 0.02155 (B) 0.05711 (C) 0.13170 (D) 0.97994

(A)

Consider the following two statements and select the correct conclusion.I. A 99% one-sample proportion confidence interval is wider than a 95% one-sample proportion confidence interval if everything else is the same.II. A one-sample proportion confidence interval with ˆp= 0.50 is wider than a one-sample proportion confidence interval with ˆp= 0.75 if everything else is the same. (A)I is True. II is True. (B) I is True. II is False. (C) I is False. II is True. (D) I is False. II is False.

(A)

Find the value of a such that P(−|a|< Z <|a|) = 0.6 (A)qnorm(0.8) (B)qnorm(0.6) (C)pnorm(0.4) (D)pnorm(0.6)

(A)

If the confidence interval for p1−p2contains only NEGATIVE numbers, it implies that (A) It is more likely that p1< p2. (B) It is more likely that p1> p2. (C) It is more likely that p1=p2. (D) None of the above are correct.

(A)

If we have a random sample x1,x2,...,xn from a population distribution, which of the following statements about the central limit theorem is correct? (A)The distribution of sample mean follows a normal distribution if the sample size is large enough for any population distribution. (B) The distribution of sample mean follows a normal distribution only if the sample size is large enough and the population distribution is normal. (C) The distribution of sample mean follows a normal distribution regardless of the sample size. (D) The distribution of sample mean follows a normal distribution only if the population distribution is normal.

(A)

In probability theory, events which can never occur together are classified as (A) Disjoint events (B) independent events (C) dependent events (D) None of the above.

(A)

In which situation would the assumptions for a hypothesis test not be met? (A) Use the data from the first 15 people who shop at Cub Foods to test if the mean grocery cost per shopper is less than $20. (B) Use data that is random and normally distributed to test if the population mean is greater than 10 (C) Use the data from a random sample of 500 students' GPA to see if the population mean GPA is 3.2 or not. (D) Use the data from a random sample of 10 normally distributed city election budgets to check if the population mean budget is not equal to 1 million USD.

(A)

Let ̄x denote the sample mean from a sample of size n= 9 from a population with mean μ= 50 and variance σ2= 9. Which of the following is true regarding the sampling distribution of ̄x? (A) ̄x has a mean of 50 and a standard deviation of1 (B) ̄x is normally distributed with a mean of 50 and a standard deviation of 1 (C) Both A and B (D) Neither A nor B

(A)

Select the incorrect description.(A)Sample variance can never be zero. (B) Median is resistant to outliers. (C) The IQR covers middle 50% of the observations. (D) None of the above.

(A)

Suppose 40% of Minneapolis citizens support Candidate B. Now assume in a sample of 100 people, 55 people responded that they support Candidate B. What is the z-score of this statistic? (Hint: What is the sampling distribution of the sample proportion?) (A) 3.06 (B) 1.02 (C) -1.02 (D) -3.06ˆP

(A)

Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. Suppose that two events are independent. ThenP(A|B) is: (A) P(A) = 0.2 (B) P(A)/P(B)= 0.5 (C)P(A)×P(B) = 0.08 (D) None of the above

(A)

Suppose the weights of newborn baby girls have a distribution with mean of 7.7pounds and standard deviation 1.2 pounds. Courtney is a newborn baby girl. Her weight has a z-score of 0.45. Which of the following is the best interpretation of her z-score? (A) Courtneys weight is 0.45 standard deviations above average. (B) Courtneys weight is 0.45 pounds above average. (C) About 45% of newborn baby girls weight less than Courtney. (D) About 45% of newborn baby girls weight more than Courtney.

(A)

The historical data shows p= 20% of students in STAT 3011 received an 'A' as their final grade. Take a sample of 100 students who have taken STAT 3011 course previously. Let ˆp be the sample proportion of students who got an 'A'. Which of the following statements about the distribution of ˆp, the sample proportion, is correct? (A)ˆp ̇∼N(0.2,√0.2∗0.8100) by the Central Limit Theorem. (B) We do not know the distribution of ˆp since Central Limit Theorem does not apply here. (C) The sample proportion ˆp is a good estimation of μ. (D) None of the above.

(A)

What level of confidence would accompany the following interval? (ˆp1−ˆp2) ± 1.0×SE(ˆp1−ˆp2) (A)***About 0.68 (B) About 1 (C) About 0.95 (D) We have to know the sample size to answer this question.

(A)

Which of the following statements is correct? (A)As long as there is a difference between a point estimate and the hypothesized value, no matter how small it is, we can always reject the null hypothesis by increasing the sample size while holding everything else constant for a hypothesis testing with Ha:μ6=μ0. (B) If the difference between a point estimate and the hypothesized value is statistically significant, the difference must be significantly large. (C) After conducting a hypothesis test, assume that the result does not support the alternative hypothesis. Then we can run another test with a different sample. If the new result is highly significant, we can ignore the first test and accept the alternative hypothesis. (D) None of above is correct.

(A)

t is known that for right-handed people, the dominant(right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference(left−right) was found. The alternative hypothesis is that left hand is stronger. The resulting test statistic was 1.80. Based on the test statistic of 1.80, select the appropriate conclusion using α = 0.05. Following R codes may be helpful. pt(1.8, df=14)=0.953 pt(1.8, df=28)=0.958 (A) Df = 14, sop-value<0.05 and the null hypothesis can be rejected. (B) Df = 14, sop-value>0.05 and the null hypothesis cannot be rejected. (C) Df = 28, sop-value<0.05 and the null hypothesis can be rejected. (D) Df = 28, sop-value>0.05 and the null hypothesis cannot be rejected.

(A)

A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head. (A) 0.15 (B) 0.25 (C) 0.50 (D) 0.75

(B)

A family has 2 children. Given that at least one of the children is a boy, what is the probability that the other child is also a boy? (A) 1/2 (B) 1/3 (C) 1/4 (D) 3/4

(B)

A manufacturer of balloons claims that p, the proportion of its balloons that burst when inflated to a diameter of up to 12 inches, is no more than 0.05. Some customers have complained that the balloons are bursting more frequently. If the customers want to conduct an experiment to dispute the manufacturer's claim, which of the following hypotheses would be appropriate? (A)H0: p6= 0.05 vs Ha: p = 0.05 (B)H0: p= 0.05 vs Ha: p > 0.05 (C)H0: p= 0.05 vs Ha: p ≠ 0.05 (D)H0: p= 0.05 vs Ha: p <0.05

(B)

A quality control group monitors the number of defects on a manufacturing line to make sure that they are meeting company standards. What statistical procedure should you use to test whether the percentage of defects is less than 0.5%? (A) Two-sided, one-sample z-test. (B) One-sided, one-sample z-test. (C) One-sided, two-sample t-test. (D) One-sided, matched-pairs t-test.

(B)

A study was conducted to see if students at University of Minnesota sleep fewer than 8 hours. The study was based on a random sample of 100 students. Suppose that the researcher obtained p-value of 0.04. Which of the following R commands will return the value of t-test statistic? (A)qt(0.02, df=99) (B)qt(0.04, df=99) (C)qt(0.96, df=99) (D)qt(0.98, df=99)

(B)

A two-sample independent t-test for testing H0: μ1=μ2 against Ha: μ1≠μ2 resulted in a p-value of 0.041. Based on this result, would the 95% confidence interval and the 99% confidence interval for μ1−μ2 contain the value 0? (A) Only the 95% confidence interval would contain 0 (B) Only the 99% confidence interval would contain 0 (C) Neither the 95% confidence interval nor the 99% confidence interval would contain 0 (D) Both the 95% confidence interval and the 99% confidence interval would contain 0

(B)

An insurance company sells a policy to airline passengers. If a flier misses the purchased flight due to medical reasons, the policy gives $300 to the flier. Otherwise, there is no return. Records show that about 5% passengers miss flight due to illness. You buy the policy for your next flight. Select the incorrect statement. (A) The expected value of the amount of money you receive is $15. (B)The standard deviation of the amount of money you receive is $50.00 (C) The amount of money you could receive is either $0 or $300. (D) None of the above.

(B)

Based on a random sample of size n= 5 drawn from a normal population, the 95% confidence interval for the population meanμis (2.00,8.00). Which of the following statements are correct? (Note: The t-multiplier for the 95% CI is 2.776 for df = 4 and 2.571 for df = 5.) i. The sample mean x is 5.00. ii. The margin of error is 3.00. iii. The standard error is 1.167. (A) i. only (B) i. and ii. (C) i. and iii. (D) i., ii. and iii.

(B)

For which of the following variables can you expect its histogram to be skewed to the right? (A) The scores of students (out of 100 points) on a very easy exam in which most score perfectly or nearly so, but only a few unprepared students score poorly. (B)Income of all adults in the United States where median household income is about $60,000 and average household income is about $117,000. (C) Heights of all female adults in Minnesota measured in centimeters. (D) All of the above.

(B)

If you roll two balanced dice simultaneously and add the sum of the dots, which of the following is most likely? (A) Getting a total of 6. (B) Getting a total of 7. (C) Getting a total of 8. (D) Getting a total of 9.

(B)

In 2014, the State of North Carolina released Henry McCollum after serving 32years in prison after DNA evidence showed that he did not rape and murder a young girl in 1983. In the US judicial system, a person is considered innocent until proven guilty. What type of error did the court make in 1983? (A) No error was made (B) Type I error (C) Type II error (D) Type III error

(B)

Let T2, T8, and Z denote the t-distribution with 2 df, the t-distribution with 8 df, and the standard normal distribution, respectively. Given that Pr(−2.5< T8<2.5) =0.963, which of the following is true? (A) Pr(−2.5< T2<2.5)>0.963 (B) Pr(−2.5< Z <2.5)>0.963 (C) Both (A) and (B) are true. (D) Neither (A) nor (B) is true.

(B)

Let pI and pM be the graduation rates from public high school in Iowa and Minnesota, respectively. Suppose a 95% Confidence Interval of pI−pM is (0.003,0.089), then: (A) It is likely pI is less than pM. (B) It is likely pI is greater than pM. (C) It is likely pI is equal to pM. (D) It is likely pM is greater than pI.

(B)

Consider the test H0: μ= 5 vs. Ha: μ ≠ 5, where the t-statistic, t= 2.46, and the sample size was 43. Then using R, which of the below would compute the correct p-value? (A)pnorm(2.46) (B)1-pt(2.46, df=42) (C)2*(1-pt(2.46, df=42)) (D)2*pt(2.46, df=42)

(C)

Select the true statement(s). (i) The large sample confidence interval for a proportion p method with a random sample of size n= 10 is still completely valid as long as the population distribution is normal. (ii) If you have a volunteer sample instead of a random, then a confidence interval for a mean μ is still completely reliable as long as the sample size is very much larger than 30. (A) Both (i) and (ii) are correct. (B) Both (i) and (ii) are incorrect (C) (i) is correct and (ii) is incorrect. (D) (i) is incorrect and (ii) is correct.

(B)

Suppose that two events A and B are independent and that event B occurs with probability 0.5. The probability that A and B both occur is 0.1. Find the probability that A or B (or both) occur. (A) 0.7 (B) 0.6 (C) 0.5 (D) Cannot be determined from the given information.

(B)

Suppose we want to test the claim that organic produce is more expensive than conventional produce. To test this, we sampled 25 different fruits and vegetables. Foreach fruit or vegetable, we took the price of its organic and conventional version. What type of test should we use to verify this claim? (A) Independent two sample z-test for difference of proportions. (B) Matched pairs t-test for mean of difference. (C) One sample z-test for proportion. (D) Independent two sample t-test for difference of means.

(B)

Suppose you buy 1 ticket out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $200. What is the expected value of winnings? (A) $0 (B) $0.20 (C) $0.50 (D) $1

(B)

The study in the previous problem showed a greater survival rate for the smokers. The best explanation is the existence of what? (A) extrapolation (B) a lurking variable (C) non constant variance (D) a nonlinear relationship

(B)

Which of the following is a population parameter? (A) s (B) β (C) r (D) None of the above.

(B)

Which of the following is not always true about the least squares regression line? (A) It passes through ( ̄x, ̄y). (B) It passes through at least one observation (x,y). (C) It passes through every (x,ˆy). (D) All the residuals sum to 0.

(B)

Which of the following sample proportion values ˆp requires the largest minimum sample size for the 95% confidence interval to have a margin of error no more than 0.05? (A) ˆp= 0.2 (B) ˆp= 0.4 (C) ˆp= 0.7 (D) They all need the same minimum sample size.

(B)

Which of the following statements is not true about the sampling distribution of a sample proportion (A) The mean does not change as sample size increases. (B) As sample size increases, standard deviation also increases. (C) If np and n(1−p) are both at least 15, then the distribution is approximately normal. (D) All of the above are not true.

(B)

t is known that for right-handed people, the dominant(right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference(left−right) was found. The alternative hypothesis is that left hand is stronger. The resulting test statistic was 1.80. This is an example of: (A) Independent two-sample t-test. (B) Matched pairs t-test. (C) One-sample z-test. (D) Independent two-sample z-test.

(B)

A Reuters story (April 2, 2003) reported that "The number of heart attack victims fell by almost 60% at one hospital six months after a smoke-free ordinance went into effect in the area (Helena, Montana), a study showed, reinforcing concerns about second-hand smoke." The number of hospital admissions for heart attack dropped from just under seven per month to four a month during the six months after the smoking ban.Select the true statements(s). i One can conclude that smoking ban causes the number of heart attack victims to drop. ii The number heart attack victims is the response variable of this study. (A) Both i and ii are true. (B) i is true and ii is false. (C)i is false and ii is true. (D) Both i and ii are false.

(C)

A diet pill company advertises that 75% of its customers lose 10 pounds or more within 2 weeks. You suspect the company of falsely advertising the benefits of taking their pills. Based on a random sample of 100 customers, 65 lost 10 pounds or more within 2weeks. The value of test statistic is 2.5. Which of the following is the correct interpretation of the test statistic? (A) If the true proportion of customers lose weight is 75%, the probability of making typeI error is 2.5%. (B) If the true proportion of customers lose weight is 75%, then the probability of obtaining as or more extreme test statistic that we observed is 2.5%. (C) If the true proportion of customers lose weight is 75%, the observed sample proportion 65% is 2.5 standard errors above the hypothesized proportion. (D) None of the above.

(C)

A sampling distribution is the probability distribution for which one of the following: (A) All values in a population (B) Observed values in a sample (C) All possible Sample statistics (D) Population parameter

(C)

Consider a hypothesis test for the population proportion: H0:p= 0.5 vsHa:p >0.5 The collected data set from a random draw has n= 100 and ˆp= 0.14. Then (A) One assumption is violated therefore we cannot consider a valid hypothesis test. (B) The assumptions are satisfied but we don't know if we can reject the null hypothesis based on the given information. (C) The assumptions are satisfied and we cannot reject the null hypothesis. (D) The test statistic follows a t distribution with 99 degrees of freedom.

(C)

Consider the 95% and 99% confidence intervals for the population proportion, computed based on the same sample. Which of the following statements is FALSE? (A) The 95% and 99% confidence intervals both contain the sample proportion. (B) If the 95% confidence interval contains the value 0.5, then the 99% confidence interval must also contain the value 0.5. (C) Compared to the95%confidence interval, the99%confidence interval will be centered at the true proportion with a higher probability. (D) Compared to the 95% confidence interval, the 99% confidence interval has a larger critical value.

(C)

Consider the following two statements and select the correct conclusion. I. Taking a random sample of size 20 is sufficient to satisfy the CLT assumptions for making a one-sample proportion confidence interval. II. Taking a random sample of size 40 is sufficient to satisfy the CLT assumptions for making a one-sample mean confidence interval. (A) I is True. II is True. (B) I is True. II is False. (C) I is False. II is True. (D) I is False. II is False.

(C)

The state of Minnesota is interested in the average age of all Minnesotan voters this most recent midterm election. The election board claims the average age of voters for midterm elections is greater than 35 years old. Suppose the state took a random sample of 200 voters and found the sample mean age was 33.5 with a sample standard deviation of 6. The state wants to test the election board's claim at a 0.01 significance level. What is the test statistic for this test? (A)−0.25 (B) 0.01 (C)−3.53 (D) 3.53

(C)

The university is interested in testing whether the proportion of undergraduate students applying to graduate school has changed compared with 5 years ago, which was about 35%. A survey was conducted and 1,000 students were randomly chosen for the survey. If we fail to find a significant difference while in fact this proportion has changed, which of the following is correct? (A) the null hypothesis was correctly accepted. (B) a Type I error has been made. (C) a Type II error has been made. (D) None of above is correct.

(C)

We are trying to estimate the mean of a population, denoted byμ. Suppose we draw a random sample from the population with size n, denoted by{X1,···,Xn}, and ̄X=(X1+···+Xn)/n is the sample mean. We use ̄X as an point estimator of μ. Which one of the following statements is true? (A) Bias of ̄X is random. (B) ̄X is a biased estimator of μ. (C) ̄Xis an unbiased estimator when we set n= 1 (D) As we increase n, then bias of ̄X will decrease.

(C)

What is an example of a continuous variable? (A) number of Facebook likes to a post (B) credit card number (C) temperature (D) population size of a city

(C)

What is the definition of bias? (A) The probability that an interval contains the parameter. (B) The interval of numbers within which the parameter value is believed to fall. (C) The difference between the mean of a statistic's sampling distribution and the true parameter value. (D) The best guess for the parameter.

(C)

Which of the following cannot be a null hypothesis? (A) μD= 0 (B) p1−p2= 0 (C) ˆp1= ˆp2 (D) μ1=μ2

(C)

Which of the following is FALSE about r2? (A) r2 measures the proportion of variability in y that is explained by its linear relationship with x. (B) r2 does not change when we reverse the roles of x and y. (C) When r2 = 0, there is no association between x and y. (D) r2 is always less than or equal to 1.

(C)

Which of the following is a continuous random variable? (A) The shoe size of a randomly selected student from STAT 3011 (B) The average number of accidents per day from last week in a randomly selected city (C) The amount of fuel used by a randomly selected car (D) All of the above

(C)

Which of the following statements about sampling distribution is TRUE? (A) A sampling distribution does not depend on the sample size. (B) A sampling distribution describes the variability in a population parameter. (C) A sampling distribution can be constructed for any statistic. (D) None of the above.

(C)

Which of the following statements is TRUE? (A) If we increase the significance levelαof a hypothesis test, the probability of making a type I error may stay the same. (B) If we increase the significance levelαof a hypothesis test, the probability of making a type II error may increase. (C) A type I error may occur when the null hypothesis is rejected. (D) For comparing the population means of multiple groups, if we perform a two-sample t-test for each pair at the α= 0.05 level, then the overall (i.e., family-wise) type I error rate may be smaller than 0.05.

(C)

Which of the following statements is always TRUE? (A) Ap-value of 0.0001 always results in rejectingH0. (B) If we rejectH0at a 0.05 significance level, then the probability thatH0is actually true is 0.05. (C) If we rejectH0at the 0.05 significance level, then we rejectH0at the 0.1significance level. (D) If we rejectH0at the 0.1 significance level, then we rejectH0at the 0.05 significance level.

(C)

Which of the following statements is incorrect? (A) When collecting data, ideally it should be possible to sample every unit of the population. (B) Statistics is the science of collecting, organizing, interpreting, and learning from data. (C)Sample variance is a parameter that describes the population. (D) A sample is a subset of the units of a population.

(C)

You are given R commands and outputs as following: > val<-c(1,2,3,4,5,6,7,8,9) > sd(val) [1] 2.7386 > t.test(x=val, conf.level=0.97, alternative="two.sided") One Sample t-test data: val t = 5.4772, df = 8, p-value = 0.0005894 alternative hypothesis: true mean is not equal to 0 97 percent confidence interval: 2.595667 7.404333 sample estimates: mean of x 5 Then, for random variable T the follows t−distribution with degrees of freedom 8, we know the probability P(T8< t) = 0.985, t is: (A) 2.738 (B) 2.500 (C) 2.633 (D) 2.404

(C)

Z-score tells us: (A) how far above or below the mean a score (x) lies (B) if the distribution a score (x) comes from is normal or not. (C)how many standard deviations above or below the mean a score (X) lies (D) Z-score doesn't tell us anything.

(C)

A 95% confidence interval for the population mean μ based on a random sample of 100 subjects was 70±2. Had the sample size been 400 instead of 100, the confidence interval would have been (no calculation needed) (A) 70±4 (B) 70±3 (C) 70±2 (D) 70±1

(D)

A hypothesis test uses two samples of size n1= 50 and n2= 50. Suppose all the assumptions of hypothesis testing are satisfied. Find the R command that returns the test statistic value that has a P-value of 0.01 when the alternative hypothesis is Ha: μ1 > μ2. (A)qt(0.01, 49) (B)pt(0.01, 99) (C)-qt(0.005, 49), qt(0.005, 49) (D)qt(0.99, 49)

(D)

A random sample of 1000 adults yields a 95% confidence interval of 6.8 to 8.0 for the mean number of close friends. Which of the following is true? (A) Ninety-five percent of adults have 6.8 to 8 close friends. (B) We are 95% confident that sample mean is between 6.8 and 8.0. (C) If we repeatedly sampled the entire population, then 95% of the time the population mean is between 6.8 and 8.0. (D) If we repeatedly sampled 1000 adults randomly, then 95% of the intervals constructed would contain the population mean.

(D)

A random survey conducted in Minnesota asked each of 1500 women whether she was a smoker. Twenty years later, a follow-up survey observed whether each woman was dead or still alive. Researchers found that 24% of the smokers died, and 37% of the non-smokers died. Which of the following is TRUE? (A) This study can be used to establish causation between smoking and survival. (B) The estimated risk of death among smokers is 24/37. (C) The estimated risk of death among non-smokers is 24/37. (D) The estimated relative risk of non-survival among smokers and non-smokers is 24/37.

(D)

A report on the nightly news broadcast stated that 25 out of 120 households with pets dogs (Group 1) were burglarized and 20 out of 160 households without pet dogs (Group 2) were burglarized. Compute the test statistic used to test the hypothesis that pet dogs are a useful deterrent to household burglaries (that is, p1< p2). (A) 1.837 (B) 1.541 (C) 2.662 (D) 1.879

(D)

A t−distribution is NOT: (A) more spread out than the standard normal distribution. (B) having 0 as its mean. (C) characterized by degrees of freedom. (D) used for constructing a CI for population proportion.

(D)

Consider testing H0: p1 = p2 vs. Ha: p1≠p2, which of the following R commands produce the p-value if the test statistic is 1.85? (A)pnorm(1-1.85) (B)pnorm(0.025) (C)pnorm(1.85) (D)2*(1-pnorm(1.85))

(D)

In a two-sided hypothesis with Ha: μ6=μ0, the p-value is found to be 0.04.Which of the following is true? (A) The 90% confidence interval would contain μ0 (B) The 95% confidence interval would contain μ0 (C) The 99% confidence interval would NOT contain μ0 (D) None of the above

(D)

Suppose that a survey is planned to estimate p1−p2 where p1 represents the proportion of male adults who are left-handed and p2 is for female. The sample data will be used to form a confidence interval. Assuming ˆp1 and ˆp2 are fixed, which one of the following combinations of sample size and confidence level will give the widest interval? (A)n1= 200, n2= 200, confidence level = 90% (B)n1= 500, n2= 500, confidence level = 90% (C)n1= 500,n2= 500, confidence level = 95% (D)n1= 200,n2= 200, confidence level = 95%

(D)

Suppose we conduct a test of H0: μ = 20 versus Ha: μ ≠ 20. The p-value is 0.06. The sample size is 50. Which of the following may be the correct value of the test statistic? (A)qnorm(0.06, mu=0, sd=1)=-1.554774 (B)-qnorm(0.03, mu=0, sd=1)=1.880794 (C)-qt(0.06, df=49)=1.582366 (D)qt(0.03, df=49)=-1.925348

(D)

The Ford Motor Company claims that its 2017 model of the Ford Escape averages 30 miles per gallon for highway driving. A group of owners of Ford Escape 2017 model wants to test this claim. Select the correct hypotheses. (A) H0: μ > 30 vs Ha: μ = 30 (B) H0: μ > 30 vs Ha: μ ≤ 30 (C) H0: μ = 30 vs Ha: μ > 30 (D) H0: μ = 30 vs Ha: μ ≠ 30

(D)

The tail area below a test statistic value z = −1.88 is 0.03 (based on the standard normal distribution). Determine which of the following statements is incorrect. (A) If the alternative hypothesis is Ha: p < p0, the data is NOT statistically significant at the α = 0.01 level. (B) If the alternative hypothesis is Ha: p < p0, the data is statistically significant at the α = 0.05 level. (C) If the alternative hypothesis is Ha: p≠p0, the data is statistically significant at theα= 0.1 level. (D) If the alternative hypothesis isHa: p≠p0, the data is statistically significant at the α= 0.05 level.

(D)

To compare the calorie content in three types of donuts - plain, sugared and frosted, researchers randomly selected 6 medium-sized (3" dia.) donuts of each type and measured the calories. The R output of Tukey's multiple comparison is given below. diff lwr upr p adj plain-frosted -23 -38.145724 -7.854276 0.0034934 sugared-frosted -13 -28.145724 2.145724 0.0983460 sugared-plain 10 -5.145724 25.145724 0.2320987 Which of the following conclusions is supported by the data? (A) Sugared donuts contain more calories than plain donuts. (B) Sugared donuts contain more calories than frosted donuts. (C) Frosted donuts contain more calories than sugared donuts. (D) Frosted donuts contain more calories than plain donuts.

(D)

Which error, Type I or Type II, would be considered more serious for decisions in the following tests? i A medical diagnostic procedure, such as mammogram to detect breast cancer. ii A trial to test a murder defendant's claimed innocence, when conviction results in the death penalty. In the American criminal justice system, a defendant is innocent until proven guilty. (A) Type I error is worse in both Case i and ii. (B) Type II error is worse in both Case i and ii. (C) Type I error is worse in Case i and Type II error is worse in Case ii. (D) Type II error is worse in Case i and Type I error is worse in Case ii.

(D)

Which of the following is a continuous variable? (A) Number of cups of coffee you drank yesterday. (B) Education level of employees in a company (C) Number of traffic tickets you received last month. (D)Amount of time you spent studying for Stat 3011 Exam 1

(D)

Which of the following is a true statement about a matched pairs study? (A) The matched pairs study controls for extra source of variability in the response variable that the two-sample t-test does not. (B) The matched pairs study can be analyzed as a one-sample t-test based on the difference in each pair. (C) The matched pairs study takes advantage of natural pairing between samples whereas the two-sample t-test does not. (D) All of the above.

(D)

Which of the following statements is correct? (A) A proportion of observations that fall in a certain category is the total number of observations divided by the count of observations in that category. (B) A discrete variable has possible values that form an interval. (C) Proportion = Percent×100 (D)A variable is any characteristic of a subject in a population.

(D)

You plan to purchase dental insurance for your three remaining years in school.The insurance makes a one-time payment of $1,000 in case of a major dental repair (such as an implant) or $100 in case of a minor repair (such as cavity). If you don't need dental repair over the next 3 years, the insurance expires and you receive no payout. You estimate the chances of requiring a major repair over the next 3 years at 5%, a minor repair as60% and no repair as 35%. LetX= payout of dental insurance. Which of the following statement is true? (A) Average payout is (1000 + 100 + 0)/3 = $366.67. (B)Xis normally distributed. (C) The probability you get at least $100 payout is 0.6. (D)None of the above.

(D)