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# Statistics: Problems and Solutions

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1.FREQUENCY DISTRIBUTION & DESCRIPTIVE STATISTICS: Open the CUMBA.xls file, which contains data from a random sample of 100 employees at Mock Company Inc. Create a Frequency Distribution of the YEARS OF EXPERIENCE for the employees using intervals of 0-4, 4-8, 8-12, 12-16 and 16-20. Also create the Descriptive Statistics for the YEARS OF EXPERIENCE. Have the output ready when you open the exam, as you will be asked questions directly from the output.

2.NORMAL: The mean amount spent by a family on food per month is \$500 with a standard deviation of \$75. Assuming that the food costs are normally distributed, what is the probability that a family spends more than \$410 per month?

3.NORMAL: A resort tracks the number of days each guest stays. They've discovered that this variable is normally distributed with a mean of 9 days and a standard deviation of 3. They would expect 10% of the guests stay longer than how many days?

4.CONFIDENCE INTERVALS: Open the CUMBA.xls file which contains data from a random sample of 100 employees at CUMBA Inc. Create a 95% confidence interval of the mean YEARS OF EXPERIENCE of employees. [Round off to 2 decimals].

5.CONFIDENCE INTERVALS: Open the CUMBA.xls file which contains data from a random sample of 100 employees at CUMBA Inc. Create a 90% confidence interval of the proportion of employees who do not have a college degree (i.e., EDUCATION LEVEL = 0).

6.SAMPLE SIZES: A bank wishes to estimate the mean balances owed by their MasterCard customers within \$75. The population standard deviation is estimated to be \$300. If a 98 percent confidence interval is used, how many cardholders should be sampled?

7.SAMPLE SIZES: Comcast wants to know the percent of their cable subscribers who use the internet at home. How large of a sample should they survey to determine the proportion who use the internet within 2% and with 90% confidence?

8. The CEO of a Fortune 500 company announced that in the past year, the average salary in his company has increased by 10%, and yet their total payroll has not increased. How is this possible, or is this an obvious lie?

9. Given a sample of 50 IQ scores ranging from 80 to 145, if the 80 were accidentally typed in error as an 8, what would be the impact on the RANGE?

1. Increase
2. Decrease
3. Remains the same

10. Given that 75% of your college students are men, and a random sample of 40 students is to be selected. You decide to randomly choose 30 men and 10 women. What type of sampling is being used?

1. Stratified sampling
2. Cluster sampling
3. Systematic sampling
4. Judgment sampling
5. Simple random sampling

11. If a manufacturer claims that their candy bar has an average of at least 10 nuts in it, and your test sample resulted in a 95% confidence interval of (8.23, 10.17), then there is evidence to suggest the manufacturer's claim is incorrect?

1. True
2. False

12. Studies have shown that 50% of people who have died have done so within 3 months of their birthday. Give a plausible reason for this phenomenon.
Paragraph:
Insert equation:

13. If the 95% confidence interval for the average age of a learner at Capella is 27.8 yrs. < MEAN < 32.6 yrs., what would your reaction be to the brochure that states the average age of a Capella learner is less than 25?
Insert equation:

14. If the 95% confidence interval of the salary of employees is (\$32000, \$40000), then 95% of the employees have a salary between 32000 and 40000.

True
False

15. Given a sample of 50 IQ scores ranging from 80 to 145, if the 80 were accidentally typed in error as an 8, what would be the impact on the MEAN?

1. Increase
2. Decrease
3. Remains the same

16. Given a sample of 50 IQ scores ranging from 80 to 145, if the 80 were accidentally typed in error as an 8, what would be the impact on the STANDARD DEVIATION?

1. Increase
2. Decrease
3. Remains the same

17. If you were told that half of the adults in the U.S. read at or below the median reading level, why shouldn't this surprise you, being the astute statistics student you are?

Insert equation

18. Given a sample of 50 IQ scores ranging from 80 to 145, if the 80 were accidentally typed in error as an 8, what would be the impact on the MEDIAN?

1. Increase
2. Decrease
3. Remains the same

19. If it is a known fact that 13% of all residential phone numbers are unlisted and you randomly select 100 numbers from the phone book, how many of the 100 do you expect to be unlisted?

20. Knowing that supervisor salaries at Acme Inc. range from \$15,000 to \$25,000 per year, what two (2) statistics can you compute about the salary from the limited information given? CHOOSE TWO.

1. MEAN
2. MEDIAN
3. MODE
4. MIDRANGE
5. STANDARD DEVIATION
6. RANGE
7. INTERQUARTILE RANGE

21. If the computed minimum sample size for an election poll were 601 people, then any 601 responses will give you the confidence level and margin of error you desire.

1. True
2. False

22. By carefully selecting a sample randomly, you can completely eliminate sampling error.

True
False

23. In measuring the salaries in a company that employs 100 factory workers along with a highly paid executive, is the MEAN or MEDIAN likely to be higher?

1. Mean
2. Median

24. What would happen to the width of the resulting confidence interval if the level of confidence is increased, from 95% to 99%?

1. Increase
2. Decrease
3. Remains the same

25. What would happen to the width of the resulting confidence interval if the sample mean is mistakenly calculated to be 64 when it should have been 46?

1. Increase
2. Decrease
3. Remains the same

26. What would happen to the width of the resulting confidence interval if the sample size is doubled, from 400 to 800?

1. Increase
2. Decrease
3. Remains the same

27. What would happen to the computed minimum sample size if the confidence level increased from 95% to 99%?

1. Increase
2. Decrease
3. Remains the same

28. What would happen to the computed minimum sample size if the tolerable sampling error increased from 2% to 5%?

1. Increase
2. Decrease
3. Remains the Same