STATISTICS FINAL

The Type I Error is called the "rejection error" in a hypothesis test since (a) this error is always made when the null hypothesis is rejected (b) this error is always made when the null hypothesis is not rejected (c) this error is possible when the null hypothesis is rejected (d) this error is possible when the null hypothesis is not rejected

(c) this error is possible when the null hypothesis is rejected

Identify the random variable as being continuous or discrete 1. time to run a marathon 2. fish in a fish tank

1. Continuous 2. Discrete

Determine whether the Events E and F are independent or dependent. (a) E: speeding on the interstate F: being pulled over by a police officer (b) E: you gain weight F: you eat fast food for dinner every night (c) E: you get a high score on a statistics exam F: The Atlanta Braves win a baseball game

(a) DEPENDENT (b) INDEPENDENT (c) INDEPENDENT

A two-tailed hypothesis test on a population proportion is conducted. The test statistic Zo is found based on the sample data. Which of the following test statistics would provide the strongest evidence against the null hypothesis? (a) Zo = 1.45 (b) Zo = -2.45 (c) Zo = -o.98 (d) Zo = 1.83 (e) Zo = 2.01

(b) Zo = -2.45 farthest from the center

According to Chebyshev's Inequality, for any distribution, what is the percentage of observations that fall within 2 standard deviations? (a) approximately 95% (b) at least 75% (c) approximately 99.7% (d) at least 89% (e) at least 68%

(b) at least 75%

In horse racing, a trifecta is a bet for which you must pick the first, second, and third place winners in their proper order to win a payoff. If there are nine horses racing, and you randomly select three as your bet in the trifecta, what is the probability that you win? (a) 0.3790 (b) 0.0014 (c) 0.7778 (d) 0.0020

(d) 0.0020

A researcher wanted to estimate the average length of time mothers who gave birth via Caesarean section spent in a hospital after delivery of the baby. (i) confidence interval of the population proportion (ii) hypothesis test of the population proportion (iii) confidence interval of the population mean (iv) hypothesis test of the population mean

(iii) confidence interval of the population mean. Because of estimation

Among 21- to 25-year-olds, 29% say they have driven under the influence of alcohol. Suppose that three 21- to 25-year-olds are selected at random 1. What is the probability that all three have driven under the influence of alcohol? (a) 0.0244 (b) 0.8700 (c) 0.2900 (d) 0.9756 2. What is the probability that at least one has not driven while under the influence of alcohol? (a) 0.0244 (b) 0.7100 (c) 0.3579 (d) 0.6241 (e) 0.9756 3. What is the probability that none of the three has driven while under the influence of alcohol? (a) 0.0244 (b) 0.3579 (c) 0.9756 (d) 0.7100 (e) 0.6241

1. (a) 0.0244 because (0.29) cubed 2. (e) 0.9756 because 1 - (0.29) cubed 3. (b) 0.3579 because (P not drive under the influence) = 1 - 0.29 = 0.71 (0.71) cubed

True or False: Sample evidence can prove a null hypothesis is true

FALSE

In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. The P(black) = 18/38 ~~0.47. This is an example of what probability? (a) classical (b) empirical (c) subjective

(a) classical

Each variable below is one of the four levels of measurement, A, B, C, D. Match each variable to the correct level of measurement. Use each level once A. Ratio B. Nominal C. Interval D. Ordinal 1. ____ Variable One: movie ratings of one star through five stars 2. ____ Variable Two: eye color 3. ____ Variable Three: volume of water used by a household in a day 4. ____ Variable Four: year of birth of college students

1. D. Ordinal 2. B. Nominal 3. A. Ratio 4. C. Interval

In a relative frequency distribution, what should the relative frequencies add up to? a) 0 b) 1 c) 100 d) the total number of observations

b) 1

In a frequency distribution, what should the frequencies add up to? a) 0 b) 1 c) 100 d) the total number of observations

d) the total number of observations

As the level of confidence of a confidence interval increases, the margin of error______

increases

Determine whether the bold value is a parameter or a statistic. The General Social Survey in 2012 asked 3,077 people whether antireligious books should be allowed in the library and found 37% thought they should be removed. (a) parameter (b) statistic

(b) statistic

If two fair dice are rolled, find the probability of a sum of 6, given that the roll is "doubles" (both dice have the same number) (a) 0.4167 (b) 0.0833 (c) 0.1667 (d) 0.1389 (e) 0.0278

(c) 0.1667

Suppose that you received a shipment of 8 tvs and 3 are defective. 2 tvs are randomly selected. 1. What is the probability of the first tv works and the second is defective? (a) 0.2344 (b) 0. 3906 (c) 0.2679 (d) 0.3571 2. What is the probability that both tvs work? (a) 0.3571 (b) 0.3906 (c) 0.2679 (d) 0.2344 3. What is the probability that both tvs are defective? (a) 0.1607 (b) 0.0938 (c) 0.7500 (d) 0.1071

1. (c) 0.2679 2. (a) 0.3571 3. (d) 0.1071

Determine whether the probabilities below are computed using classical, empirical, or subjective methods. 1. On the basis of a survey of 200 people, the probability of an individual carpooling to work is 0.11 2. According to a sports analyst, the probability that the Chicago Bears will win their next game is about 0.30 3. A pair of fair dice is rolled. The probability of rolling a seven is 1/6

1. Empirical 2. Subjective 3. Classical

A can of soda is labeled as containing 12 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under-filling the cans. Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. Which level of significance would you recommend the quality control manager use? (a) a = 0.10 (b) a = 0.05 (c) a = 0.01

(c) a = 0.01 it will be hard to reject Ho

A researcher wanted to know if a majority of Americans with a valid driver's license drive an American-made automobile. Choose the correct set of hypotheses for this hypothesis test (a) Ho: u < 0.50 H1: u > 0.50 (b) Ho: u = 0.50 H1: u > 0.50 (c) Ho: p < 0.50 H1: p > 0.50 (d) Ho: p = 0.50 H1: p > 0.50 (e) Ho: p < 0.50 H1: p = 0.50

(d) Ho: p = 0.50 H1: p > 0.50 percentage > 50%

The General Society Survey asked: "How many e-mails do you send in a day?" The results of 928 respondents indicate that the mean number of emails sent in a day is 10.4, with a standard deviation of 28.5. Given the fact that one standard deviation to the left of the mean results in a negative number of emails being sent, what shape would you expect the distribution of emails sent to have? (a) uniform (b) normal (c) skewed left (d) skewed right

(d) skewed right

For the two studies described below, determine whether each depicts an observational study or an experiment 1. Rats with cancer are randomly divided into two groups. One group receives 5 milligrams of a medication that is thought to fight cancer, and the other group receives 10 mg. After 2 years, the spread of the cancer is measured. 2. Conservation agents netted 250 large-mouth bass in a lake and determined how many were carrying parasites.

1. Experiment 2. Observational study

1. A fair coin is tossed three times in succession. The coin lands on a table and the up side of the coin is noted. Determine the sample space of the experiment using H for heads and T for tails to list the outcomes. Be sure to list all the outcomes in the sample space S: Hint: 8 outcomes 2. What is the probability of obtaining no heads? (a) 0.25 (b) 0.125 (c) 0.375 (d) 0.625 (e) 0 3. What is the probability of obtaining exactly one head? (a) 0.25 (b) 0.250 (c) 0.375 (d) 0.500 (e) 0.625 4. What is the probability of obtaining at least two tails? (a) 0.250 (b) 0.375 (c) 0.875 (d) 0.625 (e) 0.500

1. S = (HHH, HHT, HTT, TTT, TTH, THH, HTH, THT) 2. (b) 0.125 3. (c) 0.375 3/8 4. (e) 0.500 4/8

True or False: P hat is found from a random sample of size n=55 taken from a population with p=0.80. The sampling distribution is normal or approximately normal. Assume n<0.05N

FALSE

True or False: X bar is found from a random sample of size n=20 taken from a skewed population. The sampling distribution is normal or approximately normal. Assume n<0.05N

FALSE

True or False: P hat is found from a random sample of size n=60 from a population with p=0.30. The sampling distribution is normal or approximately normal. Assume n<0.05N

TRUE

True or False: X bar is found from a random sample of size n=15 taken from a normal population with no outliers. The sampling distribution is normal or approximately normal. Assume n<0.05N

TRUE

A P-value is the probability of observing a sample statistic as extreme or more extreme than the one observed assuming the (a) the null hypothesis is true (b) the alternative hypothesis is true

(a) the null hypothesis is true

For each of the following investigations, decide whether an observational study or an experiment is more appropriate. 1. Whether a special coupon attached to the outside of catalogs makes recipients more likely to order products from a mail-order catalog 2. Whether smoking has an effect on coronary heart disease 3. Whether higher SAT scores tend to be positively associated with higher college GPAs

1. Experiment 2. Experiment 3. Observational study

An investigator with the Food and Drug Administration wanted to determine whether a typical bag of potato chips contained less than 16 ounces claimed by the manufacturer. (i) confidence interval for the population proportion (ii) hypothesis test for the population proportion (iii) confidence interval for the population mean (iv) hypothesis test for the population mean

(iv) hypothesis test for the population mean. Because of the 16 ounces

True or False: X bar is found from a random sample of size n=50 taken from a skewed right population. The sampling distribution is normal or approximately normal. Assume n< 0.05N

TRUE

A 2009 study by Princeton Research found that 34% of teens text while driving. a 2020 survey conducted by Consumer Reports found that 353 of 1200 randomly selected teens had texted while driving. Based on this sample data, a 95% confidence interval for the proportion of teens who text while driving is (o.268, 0.320). Does this confidence interval provide sufficient evidence to conclude that the proportion of teens who text while driving has changed since 2009? (a) Yes (b) No

(a) Yes

According to the Centers for Disease Control and Prevention, 20.8% of high school students currently use electronic cigarettes. A high school counselor is concerned that the use of e-cigs at her school is higher. Based on sample data collected from her school, the high school counselor concludes the use of e-cigs at her school is not higher than 20.8%. Suppose, in fact, that the proportion of students at the counselor's high school who use e-cigs is 0.217. Was a Type I Error, or a Type II Error or no error committed? (a) Type I Error (b) Type II error (c) No Error

(b) Type II Error It fails to reject Ho, Ho is false. 0.217>0.208

In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, 2 slots are green. We watched a friend play roulette for two hours. In that time, we noted that the wheel was spun 50 times and that out of those 50 spins, black came up 22 times. Based on this data, the P(black) = 22/40 = 0.44. This is an example of what type of probability? (a) classical (b)empirical (c) subjective

(b) empirical

When selecting the critical t-score for a confidence interval for the population mean, the degrees of freedom equal (a) n, where n is the sample size (b) n - 1, where n is the sample size (c) n - 2, where n is the sample size (d) s/squre root of n

(b) n - 1, where n is the sample size

Determine whether the bold value is a parameter or a statistic. The job placement office at your school surveys all graduating seniors at the school and finds the percentage of students with entry level jobs earning more than $45,000 a year is 62%. (a) parameter (b) statistic

(b) statistic

I conduct a statistical test of hypotheses, determine the P-value, and find that the null hypothesis will be rejected if the level of significance is 0.05. Then I may conclude that (a) the null hypothesis would be rejected at the 0.01 significance level (b) the null hypothesis would be rejected at the 0.10 significance level (c) both a and b are true (d) none of the above are true

(b) the null hypothesis would be rejected at the 0.10 significance level P-value< 0.05< 0.10

At the Acme Corporation, the mean salary of all employees is $58,000 and the standard deviation is $7,000. Assuming that the distribution salaries is bell-shaped, according to the Empirical Rule, approximately 99.7% of employees have a salary between (a) $47,500 to $68,500 (b) $51,000 to $ 65,000 (c) $37,000 to $79,000 (d) $44,000 to $72,000

(c) $37,000 to $79,000 u +- 3sigmaO 58,000 +- 3(7,000)

At the U.S. Open Tennis Championship, a statistician keeps track of every serve that a particular player hits during the tournament. The statistician reported that for this tennis player, the mean serve speed was 92 mph and the serve speed distribution was skewed right. Which of the following values is most likely the value of the median serve speed? (a) 110 mph (b) 95 mph (c) 85 mph (d) 103 mph (e) 99 mph

(c) 85 mph median<mean median<92

An official with the Internal Revenue Service wished to estimate the proportion of high-income (greater than $100,000 annually) earners who under-reported their net income (and, therefore, their tax liability). (i) confidence interval for the population proportion (ii) hypothesis test for the population proportion (iii) confidence interval for the population mean (iv) hypothesis test for the population mean

(i) confidence interval for the population proportion

In 2014, of the 37 million borrowers who have outstanding student loan balances, 14% have at least one past due student loan account. A researcher with the United States Department of Education believes this percentage has increased since then. (i) confidence interval for the population proportion (ii) hypothesis test for the population proportion (iii) confidence interval for the population mean (iv) hypothesis test for the population mean

(ii) hypothesis test for the population proportion

As the sample size used to obtain a confidence interval increases, the width of the interval_____

decreases