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Statistics 13 C Spring 2009

Practice Midterm2

Instruction: You have 50 minutes to work on this exam. It is closed book and one page of formula is provided with the exam. You may use your hand held calculator. The exam has 16 multiple choice problems. Please, hand in BOTH the marked hardcopy and scantron form. You need to MARK your answers on BOTH. A blank hardcopy is NOT acceptable. We will NOT accept scantron only. The grading is based on the scantron which will NOT be returned to you. This is version A, please mark the corresponding circle on the scantran.

1) Which statement best describes a parameter?

A) A parameter is a sample size that guarantees the error in estimation is within acceptable limits.

B) A parameter is an unbiased estimate of a statistic found by experimentation or polling.

C) A parameter is a numerical measure of a population that is almost always unknown and must be estimated.

D) A parameter is a level of confidence associated with an interval about a sample mean or proportion.

2) The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a period. The director randomly selects 49 different periods and determines the number of admissions for each. For this sample, [pic]=15.8 and s=5. Estimate the mean number of admissions per period with a 99% confidence interval.

A) 15.8 ± . 707

B) 15.8 ± . 263

C) 15.8 ± 9.196

D) 15.8 ± 1.839

3) The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 200 students who park in the chosen lot on a given day. The confidence interval is

A) meaningful because the sample is representative of the population.

B) meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures normality of the sampling distribution of the sample mean.

C) not meaningful because the sampling distribution of the sample mean is not normal.

D) not meaningful because of the lack of random sampling.

4) A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood.

X = sale_price

SAMPLE MEAN OF X = 46,500

SAMPLE STANDARD DEV = 13,747

SAMPLE SIZE OF X = 15

CONFIDENCE = 99

UPPER LIMIT = 57,066.7

SAMPLE MEAN OF X = 46,500

LOWER LIMIT = 35,933.3

Which of the following is a practical interpretation of the interval above?

A) 99% of the homes in this neighborhood have sale prices that fall between $35,933.30 and $57,066.70.

B) We are 99% confident that the mean sale price of all homes in this neighborhood falls between $35,933.30 and $57,066.70.

C) We are 99% confident that the true sale price of all homes in this neighborhood fall between $35,933.30 and $57,066.70.

D) All are correct practical interpretations of this interval.

5) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 65 have laptops. What assumptions are necessary for this test to be satisfied?

A) The population has an approximately normal distribution.

B) The sample size n satisfies both np0 ≥ 15 and nq0 ≥ 5.

C) The sample size n satisfies n ≥ 30.

D) The sample proportion is close to .5.

6) The confidence interval at the 95% level of confidence for the population proportion if a sample of size 100 had 30 successes is:

A) (0.2102, 0.3102)

B) (0.2102, 0.3898)

C) (0.2959, 0.3041)

D) (0.2595, 0.3405)

7) A company tests all brands of golf balls to ensure that they meet certain specifications. One test conducted is intended to measure the average distance travelled when the ball is hit by a machine. Suppose the company wishes to estimate the mean distance for a new brand to within 1.7 yards with 95% confidence. Past tests indicate that the standard deviation of the distances is approximately 11yards. How many golf balls should be hit by the machine to achieve desired accuracy in estimating the mean?

A) 153

B) 161

C) 165

D) 172

8) A Type I error is committed when we:

A) Reject a true null hypothesis

B) Reject a false null hypothesis

C) Don’t reject a false null hypothesis

D) Don’t reject a true null hypothesis

9) A government testing agency studies aspirin capsules to see if customers are getting cheated with capsules that contain lesser amounts of medication than advertised. Suppose the testing agent concludes the capsules contain a mean amount below the advertised level when in fact the advertised level is the true mean. Which type of error, if any, did the testing agency commit?

A) This is a Type I error.

B) This is a Type II error.

C) This is a correct decision.

D) Need more information to answer this question

10) In testing the hypotheses[pic], the following information is known: n = 64, [pic]=78, and s = 10. The test statistic is equal to:

A) +1.96

B) +2.4

C) -2.4

D) –1.96

11) As the degrees of freedom for the t distribution increase, the distribution approaches

A) The value of zero for the mean.

B) The t distribution.

C) The normal distribution.

D) The binomial distribution.

12) Consider the following set of salary data:

[pic]

Which assumption is necessary to perform a test for the difference in population means?

A. The population variances of salaries for men and women are equal.

B. The two samples were independently selected from the populations of men and women.

C. Both of the target populations have approximately normal distributions.

D. The means of the two populations of salaries are equal.

13) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 20 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below:

[pic] = 2.09 [pic] = 1.99 [pic] = .10

[pic] = 0.22 [pic] = 0.19 [pic] = .03

Assuming a matched pairs design, which of the following assumptions is necessary for a confidence interval for the mean difference to be valid?

A. The samples are randomly and independently selected.

B. The population variances must be equal.

C. The sample variances must be equal.

D. The population of paired differences has an approximate normal distribution.

14) A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Suppose the following 95% confidence interval for [pic] was calculated: (100, 2500). Which of the following inferences is correct?

A. We are 95% confident that no significant difference exists in the mean number of hours of continuous use before breakdown of engines using oils A and B.

B. We are 95% confident that an engine using oil B has a higher mean number of hours of continuous use before breakdown than does an engine using oil A.

C. We are 95% confident that the mean number of hours of continuous use of an engine using oil A is between 100 and 2500 hours.

D. We are 95% confident that an engine using oil A has a higher mean number of hours of continuous use before breakdown than does an engine using oil B.

15) The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful energy at a lower cost. The cost is measured by plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less the industrial plant pays for delivered energy. Suppose we wish to determine if there is a difference in the average investment/quad between using electricity and using gas. Our null and alternative hypotheses would be:

A. [pic]: ([pic] - [pic]) = 0 vs. [pic]: ([pic] - [pic]) < 0

B. [pic]: ([pic] - [pic]) = 0 vs. [pic]: ([pic] - [pic]) ≠ 0

C. [pic]: ([pic] - [pic]) = 0 vs. [pic]: ([pic] - [pic]) = 0

D. [pic]: ([pic] - [pic]) = 0 vs. [pic]: ([pic] - [pic]) > 0

16) Refer to problem 15. Random samples of 11 plants using electricity and 16 plants using gas were taken, and the plant investment/quad was calculated for each. In an analysis of the difference of means of the two samples, the owners were able to reject H0 in the test [pic] vs. [pic] . What is our best interpretation of the result?

A. The mean investment/quad for electricity is not different from the mean investment/quad for gas.

B. The mean investment/quad for electricity is less than the mean investment/quad for gas.

C. The mean investment/quad for electricity is different from the mean investment/quad for gas.

D. The mean investment/quad for electricity is greater than the mean investment/quad for gas.

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