Practice Questions and Answers in Statistics

Estimating the Mean Cholesterol Levels of Heart Patients

You wish to estimate the mean cholesterol levels of patients two days after they had a heart attack. To estimate the mean, you collect data from 28 heart patients. Justify for full credit.
(a) Which of the followings is the sample?
(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two days ago
(ii) Cholesterol level of the person recovering from heart attack suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered two days ago
(iv) Set of 28 patients recovering from a heart attack suffered two days ago
(b) Which of the followings is the variable?
(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two days ago
(ii) Cholesterol level of the person recovering from heart attack suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered two days ago
(iv) Set of 28 patients recovering from a heart attack suffered two days ago.

2. Choose the best answer. Justify for full credit.
(a) The Knot.com surveyed nearly 13,000 couples, who married in 2017, and asked how much they spent on their wedding. The average amount of money spent on was $33,391.
The value $33,391 is a:
(i) parameter
(ii) statistic
(iii) cannot be determined from information provided.
(b) A marketing agent asked people to rank the quality of a new soap on a scale from 1 (poor) to 5 (excellent). The level of this measurement is
(i) nominal
(ii) ordinal
(iii) interval
(iv) ratio

3. True or False. Justify for full credit.
(a) If the variance from a data set is zero, then all the observations in this data set must be identical.
(b) The median of a normal distribution curve is always zero.
4. A STAT 200 student is interested in the number of credit cards owned by college students She surveyed all of her classmates to collect sample data.
(a) What type of sampling method is being used?
(b) Please explain your answer.

5. A study was conducted to determine whether the mean braking distance of four-cylinder cars is greater than the mean braking distance of six-cylinder cars. A random sample of 20 four- cylinder cars and a random sample of 20 six-cylinder cars were obtained, and the braking distances were measured.
(a) What would be the appropriate hypothesis test for this analysis?
(i) t-test for two independent samples
(ii) t-test for dependent samples
(iii) z-test for population mean
(iv) correlation
(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach?

6. A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. The researcher wants to test the claim that all ten programs are equally effective in weight loss.
(a) Which statistical approach should be used?
(i) confidence interval
(ii) t-test
(iii) ANOVA
(iv) Chi squar

(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach?

7. A STAT 200 professor took a sample of 10 midterm exam scores from a class of 30 students The 10 scores are shown in the table below:
(a) What is the sample mean?
(b) What is the sample standard deviation? (Round your answer to two decimal places)
(c) If you leveraged technology to get the answers for part (a) and/or part (b), what technology did you use? If an online applet was used, please list the URL, and describe the steps. If a calculator or Excel was used, please write out the function.
8. There are 15 members on the board of directors for a Fortune 500 company. If they must select a chairperson, a first vice chairperson, a second vice chairperson, and a secretary.
(a) How many different ways the officers can be selected?
(b) Please describe the method used and the reason why it is appropriate for answering the question. Just the answer, without the description and reason, will receive no credit.

9. Amy has six books from the Statistics is Fun series. She plans on bringing two of the six books with her in a road trip.
(a) How many different ways can the two books be selected?
(b) Please describe the method used and the reason why it is appropriate for answering the question. Just the answer, without the description and reason, will receive no credit.
10. There are 4 suits (heart, diamond, clover, and spade) in a 52-card deck, and each suit has 13 cards. Suppose your experiment is to draw one card from a deck and observe what suit it is. Express the probability in fraction format. (Show all work. Just the answer, without supporting work, will receive no credit.)