# DATA205 Exam 2 (July 2019) solution file attachment(s)

`Preview of EXAM-2.docx`
in     Â Billy   not get     Question       3   would you     area       two   z-scores on     curve?Selected       area   need to     z       scores   Find the     each       side   the mean)     mean       smaller   from the     Correct       areas   each z-score     out       canâ€™t   random sample     directly       population   to see     are       Limit   tells us     sample       the   as the     Correct       to   error Â Thus     “eyeball”Â or       the   between the     and       testing   significance Question     of       to   standard error     sample       increase   N?Selected Answer:As     the       decrease   Standard error     mean       the   standard deviation     the       N   Answer:Â When you     sample       the   of sampling     standard       lowered   a larger     254       pointsA   reports that     confidence       â€œstatistically   â€Â What statistical     she       all   samples would     same

DATA 205 Introductory Analytics (QC)

Exam 2

Question 1A defining characteristic of the normal curve is that it is

a. theoretical.

b. perfectly nonsymmetrical.

c. positively skewed.

d. negatively skewed.

Question 2A sample selected according to the principle of EPSEM is extremely likely to be

a. inaccurate.

b. biased.

c. large.

d. representative.

Question 3By definition, the normal curve is

a. empirical.

b. positively skewed.

c. negatively skewed.

d. symmetrical.

Question 4By the theorems presented in the text, we know that the mean of a sampling distribution of sample means will be

a. close to the value of the sample mean.

b. representative of the entire population.

c. the same as the population mean.

d. between the population and sample means in value.

Question 5Converting scores into Z scores standardizes the original distribution to units of the

a. median.

b. percentage.

c. mean.

d. standard deviation.

Question 6In systematic random sampling, the researcher randomly selects

a. cases according to their scores.

b. the first case and every kth case thereafter.

c. every other case.

d. cases following any systematic pattern.

Question 7In the normal curve, the mean is?

a. ?equal to the median and mode.

b. greater than the mode.

c. ?greater than the median.

d. ?less than the median.

Question 8On all normal curves the area between the mean and Â± 1 standard deviation will be

a. about 68% of the total area.

b. about 34% of the total area.

c. 50% of the total area.

d. 99.9% of the total area.

Question 9Social scientists gather data from samples instead of populations because

a. samples are much larger and more complete.

b. samples are more meaningful and interesting.

c. samples are more trustworthy.

d. populations are often too large to test.

Question 10The shape of the sampling distribution of sample means can be assumed to be normal when N is

a. a large percentage of the population.

b. at least twice the value of the population standard deviation.

c. 100 or more.

d. any number as long as you know the value of the population mean.

Question 11Unless a sample is __________, it cannot be used to make accurate generalizations to a population.

a. representative

b. very small

c. stratified

d. very large

Question 12The most commonly used confidence level is

a. 90.5%

b. 99.5%

c. 95%

d. 90%

Question 13A confidence level of 99% is the same as an alpha level of

a. 0.001

b. 0.10

c. 0.05

d. 0.01

Question 14

All other things being equal, larger sample will cost more to process

Answers: a. and will always produce narrower confidence intervals.

b. but will not necessarily have narrower confidence intervals.

c. but will produce more precise intervals if the confidence level is low.

d. and will always produce wider confidence intervals.

Question 15The width of an interval estimate can be controlled by

a. changing the confidence level.

b. changing the alpha level.

c. changing the sample size.

d. Any of the above

Question 16A one-tailed test of significance could be used whenever

a. the researcher feels like it.

b. the researcher can predict a direction for the difference.

c. the null hypothesis is thought to be true.

d. the alpha level exceeds 0.10.

Question 17Do sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers? The appropriate test of this hypothesis would be

a. a one-tailed test.

b. participant observation.

c. a two-tailed test.

d. cross-sectional.

Question 18 If we reject a null hypothesis which is in fact true, we

a. should have used a one-tailed test.

b. have made a Type I error.

c. have made a Type II error.

d. have made a correct decision.

Question 19 In most cases, a researcher sets out to?

a. ?prove the null hypothesis.

b. ?disprove the null hypothesis.

c. ?disprove the research hypothesis.

d. ?prove the research hypothesis.

Question 20 In terms of hypothesis testing, “significance” refers to the?

a. ?difference between an independent and dependent variable.

b. ?difference between the two independent variables.

c. ?difference between the sample and population values.

d. ?difference between our observed and our predicted outcomes.

Question 21 A schoolâ€™s athletics department only has enough money to fund awards for its top two athletes. The awards will be distributed based on the relative performance of each player within their sport. The head of the athletics department asks the team coaches for information on the most valuable players are on each sports team.

Sarah is the top player on the bowling team, she consistently bowls a score of 220. The mean bowling score in the conference is 187 with a standard deviation of 15. Her z-score is +2.20

Billy is the highest scoring player on the soccer team. He had 25 goals this season. The conference average (among leading scorers) was 11 goals with a standard deviation of 7. His z-score is +2.00

Tom is the player with the most runs scored on the baseball team. He scored 29 runs this season. The conference average runs scored is 15 with a standard deviation of 6. His z-score is +2.33

Based on their individual performances, who will NOT get the money? Explain your choice.

Question 22 How would you find an area that is between two positive z-scores on the normal curve?

Question 23Why canâ€™t a random sample mean be directly compared to a population mean to see if they are different?

Question 24What happens to the standard error of a sample mean when you increase the N?

Question 25A researcher reports that using 99% confidence her finding is â€œstatistically significant.â€

What statistical decision did she make?

What percent of all possible samples would have the same conclusion?

What is the probability that her conclusion is incorrect?

Question 26The Monitoring the Future (MTF) project began in 1975. The MTF studies changes in the beliefs, attitudes, and behavior of young people in the United States. The survey samples 12th grade students from across the United States.

Below is output for GPA from the most recent sample of 12th graders:

What is the point estimate of the population mean based on the output above?

What confidence level was used in this analysis?

Question 27A boat manufacturing company wants to know how long people own their boats before purchasing a new one. A random sample of 160 boat owners showed that, on average, they own a boat for 8.5 years, with a standard deviation of 3.55 years, before they purchase a new boat. Using a 99% confidence level, what is the mean length of boat ownership for all boat owners?

(Show all work below including formula(s) and calculation(s))

Question 28In a random sample of 23 private school teachers in Queens County, the average teaching experience is 8.4 years with a standard deviation of 3.02 years. In the State of New York, private school teachers have a mean of 9.6 years of teaching experience. Are the private school teachers in Queens County significantly less experienced than all private school teachers in New York State?

(Show all work below including formula(s) and calculation(s))

Question 29 An auto manufacturer followed the repair records of the cars manufactured in a new plant and found that they had an average of 7 repairs with a standard deviation of 4 before the warranties expired. Assume that the number of repairs is normally distributed.

What percent of the cars from this plant would have over 10 repairs?

If 450 cars of the cars sold were manufactured at this plant, how many of them would have over 10 repairs?