Stat Midterm Example

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  • Topic: Arithmetic mean, Standard deviation, Normal distribution
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Department of statistics

Statistics for Business, Stat 130
Midterm exam
November 15, 2011

Form B

Name:| I.D. Number:|


* Write your name and student ID.
* You have one hour and thirty minutes to complete the exam. * You may use a formula sheet and a calculator. No other outside materials are allowed. * There are seven problems in the exam.

* Total score of points is 20.

Problem 1:(5 points) Multiple-choice questions:

Question 1: If A and B are mutually exclusive events, with P(A) = 0.6 and P(B) =0 .4, then P(A and B) is:

a. 0.50
b. 0.00
c. 0.24
d. 1.00

Question 2: As the sample size, n, increases, what happens to the shape of the sampling distribution of the means?

a. approaches the uniform distribution
b. positively skewed
c. approaches a normal distribution
d. negatively skewed

Question 3: Which of the following statements is correct?

a. A point estimate is an calculated from the population
b. A point estimate is an estimate of the range of a population parameter c. A point estimate is a single value estimate of the value of a population parameter d. All of the above

Question 4: Sampling distributions describe the distribution of

a. sample statistics
b. population parameters
c. neither parameters nor statistics
d. both parameters and statistics

Question 5: A 90% confidence interval estimate for a population mean is determined to be 65.48 to 76.52. If a 95% confidence interval for is constructed, it must be:

a. the same as the 90% confidence interval
b. wider than the 90% confidence interval
c. narrower than the 90% confidence interval
d. There is not enough information to answer this question


Question 6: If all possible samples of size n are drawn from a population, the probability distribution of the sample means is called the:

a. sampling distribution of sample means
b. standard error of the sample mean
c. normal distribution
d. expected value of the sample mean

Question 7: If a sample of size 144 is taken from a population whose standard deviation is equal to 60, then the standard error of the mean is equal to

a. 0.41667
b. 144
c. 5
d. None of the above

Question 8: Which of the following statements are always correct?

a. P(A and B) = P(A) . P(B)
b. P(A or B) = P(A) + P(B) - P(A and B)
c. P(A) = 1-P(A)
d. P(A or B) = P(A) + P(B)

Question 9: A basketball player makes 70 percent of his free throws during the regular season. Consider his next 10 free throws. What is the expected number of free throws that he will make?

a. 5.6
b. 2.0
c. 7.0
d. 1.2

Question 10: Suppose P(A) = 0.65. The probability of complement of A is:

a. -0.35
b. 0.35
c. -0.65
d. 0.65

Problem 2: (2.5 points). A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning systems electrical problem| gas leaks| Total|
| Yes| No| |
Yes| 56| 24| 80|
No| 14| 6| 20|
Total| 70| 30| 100|
If this is a representative sample of AC failure, find the probability that:

a. (1/2 point)The failure involves a gas leak.

b. (1/2 point)There is an electrical problem given that there was a gas leak.

c. (1/2 point)There is at least one of the failures.

d. (1 point)Does gas leak depend on electrical failure? Explain?

Problem 3: (1.5 points)

The following table contains the probability distribution for the number of traffic accidents daily (Y) in a small city. y| 0| 1| 2| 3| 4| 5|
p(y)| 0.05| 0.15| ….| 0.40| 0.10| 0.05|

a. (1/2 point)Find the probability that Y equals 2.

b. (1 point)Compute the mean of Y.

Problem 4: (1.5 points). An official from the securities commission estimates that 65% of all investment bankers have profited from the use of insider...
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