Basic Statistics ECOE 1323

Basic Statistics ECOE 1323

Spring 2007

Final Exam

Name:______ID Number:______

Instructions:

Write your name and student ID.
You have 2 hours
This exam must be your own work entirely. You cannot talk to or share information with anyone.
Show all your work. Partial credit will only be given where sufficient understanding of the problem has been demonstrated and work is shown.

Don't Write on This Table

Question / #1 / #2 / #3 / #4 / Bonus / Total
Points

Section I: Multiple-Choice

For each question in this section, circle the correct answer. (Problem is worth 2 pts.)

1.The distinction between descriptive and inferential statistics is that

a) descriptive statistics are numeric, inferential statistics are graphic.

b) descriptive statistics are mean-based, inferential statistics are median-based.

c) descriptive statistics describe data sets, inferential statistics involve generalizing to

populations.

d) descriptive statistics are used in social science, inferential statistics are used in physical

sciences.

e) None of these.

2. For which of the following statistics would one not need to put the data in orderfrom smallest to largest?

a) the interquartile range

b) the trimmed mean

c) the median

d) the range

e) the variance

3. Suppose that for a set of numeric data, where the numbers are not all different, the standard deviation is less than 1.0. Then it must be true that

4. Which of the following indicates that an association between x and y is positive?

a) A positive coefficient of determination

b) A positive standard deviation about the least squares line

c) A positive intercept of the least squares line

d) A positive Pearson’s correlation coefficient

e) A positive residual sum of squares

5. The slope of the regression line and the correlation between two variables is related in the following way:

a) The slope is always greater in absolute value than the correlation.

b) The slope and correlation must be of the same sign.

c) The slope and correlation must be of different sign.

d) The slope is always less in absolute value than the correlation.

e) None of (a) - (d) is necessarily true.

7. The event, not A is called the ______of event A.

a) negation

b) complement

c) union

d) intersection

e) conjunction

For questions 8 - 9, let x denote the number of accidents in a given month at a certain high school parking lot. Suppose that the probability distribution of x is:

x / 0 / 1 / 2 / 3 / 4 / 5
P(x) / .110 / .215 / .260 / .214 / .134 / .067

8. What is the probability that there are fewer than 3 accidents in a given month?

a) .201 b) .214 c) .585 d) .799 e) None of these

9. What is the probability that 2 to 4 (inclusive) accidents occur in a given

month?

a) .126 b) .134 c) .394 d) .608 e) None of these

10. Which of the following statements about normal curves is false?

a) Every normal curve is symmetric.

b) Every normal curve is symmetric about 0.

c) Every normal curve is bell-shaped.

d) Every normal curve is centered at its mean.

e) About 0.68 of the area under a normal curve is within 1

standard deviation of its mean.

12. Which of the following is not a property of a binomial experiment?

a) It consists of a fixed number of trials, n.

b) Outcomes of different trials are independent.

c) Each trial can result in one of several different outcomes.

d) Observations consist of the number of successes for each trial of the

experiment.

e) The probability of success is constant for each trial.

14. Suppose that x has a probability distribution with density function

. Then the value of c is:

a) 0.5 b) 0.6 c) 0.7 d) 0.8 e) 0.9

16. Which of the following is not a statistical hypothesis?

17. A type I error is made by

a) rejecting when it is true.

b) rejecting when it is false.

c) failing to reject when it is true.

d) failing to reject when it is false.

20.The degrees of freedom of a paired t test based on n = 10 pairs is

a) 9 b) 10 c) 19 d) 20 e) None of these

Section II: Free Response Problems

Question (1)

(I) A reporter for a student newspaper is writing an article on the cost of attending college. A portion of the article deals with the cost of off-campus housing. A sample of 10 one-bedroom units within one-half mile of campus resulted in a sample mean of $350 per month and a sample standard deviation of $30, assuming that the population is normally distributed.

(a)[5 Points] Provide a 95% confidence interval estimate of the population mean.

(b)[8 Points]The college newspaper claims that mean cost per month for one-bedroom units within one-half mile of campus is less than $370. Test this claim at 0.05 level of significance.

(II) [7 Points] To estimate the proportion of traffic deaths in Florida last year that were alcohol related, determine the necessary sample size for the estimate to be accurate to within .05 with probability 0.99. Based on results of a previous study, we expect the proportion to be about 0.35.

Question (2)

(I) [10 Points]In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01 level, test the claim that the failure rate is now lower if a random sample of 1520 current job applicants results in 58 failures.

Ha:

Test Statistic:

P-value:

Conclusion:

(II) [10 Points] How large a sample size is needed to estimate the mean annual income of Native Americans correct to within $2000 with probability .99? Suppose there is no prior information about the standard deviation of annual income of Native Americans, but we guess that about 68% of their incomes are between $10000 and $40,000 and that this distribution of incomes is approximately mound shaped.

Question (3)

(I) [10 Points]The Montana Highway Patrol is interested in determining whether Montana residents or nonresidents drive faster on a particular stretch of Interstate 90. Independent random samples of the speeds of cars having Montana license plates and cars licensed in other states results in the summary data listed below.

Group / Sample size / Sample Mean / Sample standard deviation
Montana / 14 / 73.2 / 3.8
Others / 17 / 76.6 / 4.7

Assume the population variances are the same. At 0.05 level of significance, is there sufficient evidence to conclude that nonresidents drive faster on this stretch of Interstate 90 than residents of Montana?

Ha:

Test Statistic:

P-value

Conclusion:

(II) [10 Points] An article reports that (4.0, 5.6) is a 95% confidence interval for the mean length of stay, in days, of patients in hospital for a particular operation. The article reports the sample size of 50, but not the sample mean or standard deviation. Find them.

Bonus:

(I) [3 Points] For a normally distributed variable, verify that the probability between and equals .50

(II) [3 Points] Find the z-value such that the interval and contains 98% of the probability for a normal distribution.

(III)A fast food chain sells hamburger that they claim has sodium content of 650 milligrams. A simple random sample of 35 hamburgers was analyzed for sodium content. A 99% confidence interval for the population mean sodium content, , of such hamburgers is (652, 672). Answer the following questions with yes, no or can't tell. Give an explanation for your answer.

(a)[2 Point] Does the population mean lie in the interval (652, 672)?

(b)[2 Point] If we were to use the preceding data to test the hypotheses

Ho:  =650 versus Ha: 650. At a 1% significance level, would we reject the null hypothesis? Explain.

Formulas:

Population mean (s) / Level C confidence interval / Hypothesis test
Large sample
One-sample z test
Use s if is unknown / /
Small sample and unknown
One-sample t test /
/ ,
Large samples
Two-sample z test
Use s1 and s2 if are unknown / /
Pooled two-sample t test

unknown & equal /
/

Two-sample t test
unknown & unequal /
/

Matched pairs t-test

/ , ,
One-Proportion z test /
where Wilson Estimate /
where the Sample proportion
Computing P-values / Use -table for tests and t-table for t tests
Reject if P-value
Sample size for desired margin of error m
One-sample interval:
/ One-proportion interval: