Download Midterm 2 with solution

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Statistics 13A Summer Session II 2009
Midterm 2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Suppose a coin is tossed four times. Let X denotes the total number of heads obtained in the four tosses. What
are the possible values of the random variable X?
A) 4
B) 1, 2, 3, 4
C) 0, 1, 2, 3, 4
D) 0, 1, 2
E) 1, 2
2) Refer to problem 1, what is the probability to get exactly 2 heads?
A) 1/16
B) 3/8
C) 1/2
D) 3/16
E) 1/4
3) Find the standard deviation of the binomial random variable. On a 10-question multiple choice test, each
question has four possible answers, one of which is correct. For students who guess at all answers, find the
standard deviation for the random variable X, the number of correct answers.
A) 1.369
B) 1.875
C) 2.045
D) 1.972
E) 1.684
4) Find the mean of the binomial random variable. A die is rolled 21 times and the number of twos that come up
is tallied. If this experiment is repeated many times, find the mean for the random variable X, the number of
twos.
A) 2.5
B) 10.5
C) 6.5
D) 3.5
E) 7.0
5) A professional shooting player has shot 70% of his targets during his career. If he shoots 3 targets in tonight's
game, what is the probability that he fails on each shot?
A) 0.027
B) 0.857
C) 0.729
D) 0.030
E) 0.001
6) Assume that the heights of women are normally distributed with a mean of 65.2 inches and a standard
deviation of 3.0 inches. What proportion of women is between 61.0 and 67.9 inches tall.
A) 0.3351
B) 0.6037
C) 0.2649
D) 0.5257
E) 0.7351
7) If a data set is normally distributed, what is the approximate proportion of measurements you would expect to
fall within µ ± 2σ?
A) 100%
B) 95%
C) 68%
D) 99%
E) 50%
8) Find the z-score having area 0.33 to its right under the standard normal curve.
A) 0.6915
B) -0.44
C) -0.6915
D) 0.44
E) 0.7915
9) A chocolate company claims that 25% of its chocolate candies are dark chocolate. Suppose that the chocolate
candies are packaged at random in small bags containing 200 candies. Describe the sampling distribution
model of the proportion of dark chocolates in a bag.
A) mean =. 75; standard error = 0.0310
B) There is not enough information to describe the distribution.
C) mean =. 25; standard error = 0.0201
D) mean =. 75; standard error = 0.0210
E) mean = .25; standard error =0.0306
10) Assume that the student fees in the United States are normally distributed with a mean of $30,000 and a
standard deviation of $3000. If 225 students are randomly selected, find the probability that their mean
fees are greater than $30500.
A) 0.9938
B) 0.0045
C) 0.0054
D) 0.0062
E) 0.9946
11) When determining the sample size for estimating a population mean for a given previously known variance
and a desired margin of error, a bigger the confidence level,
A) has an undeterminable effect on the sample size required.
B) the larger the sample size is required for the desired margin of error
C) the smaller the sample size required for the desired margin of error
D) has no effect on the sample size required.
E) has an effect on the sample size only if the mean is negative.
12) The width of a confidence interval estimate for a mean will be
A) narrower for a sample of size 200 than for a sample of 100
B) wider for 80% confidence than for 99% confidence.
C) wider when the variance is 0.4 than when it is 0.9.
D independent of sample size.
E) independent of the confidence level.
13) In a survey of 400 professional football players, 350 were opposed to the use of camera for addressing offside
issues. Find the margin of error that corresponds to a 99% confidence interval (round to 3 digits).
A) 0.51
B) 0.028
C) 0.043
D) 0.28
E) 0.43
14) A 95% confidence interval for the mean grade of midterm one is (13.8, 25.2). What is the point estimate of the
mean grade of midterm one?
A) 23.6
B) 14.5
C) 25.2
D) 19.5
E) 14.1
15) In a survey of 400 people who suffer occasionally from migraine headaches in a certain city, 60% said that
they get relief from taking ibuprofen. The margin of error in the survey was reported as 5 percentage points
(with a 90% degree of confidence). Which statement is correct?
Not enough information to determine whether the margin of error is consistent with the sample size.
B) The reported margin of error is consistent with the sample size.
C) The stated margin of error could be achieved with a smaller sample size.
D) The sample size is too small to achieve the stated margin of error.
E) The stated margin of error can only be achieved with a larger sample size.
16) Using t-tables, report the t-score for the 90% confidence interval with df = 17.
A) 2.645
B) 1.96
C) 3.746
D) 1.645
E) 1.74
17) From a sample of 200 items, 12 items are defective. The point estimate of the population proportion defective
will be:
A) 12
B) 0.12
C) 0.06
D) 16.67
E) 0.062
18) Of 257 randomly selected statistics graduate students, 72 said that they planned to work as university
faculty. Construct a 99% confidence interval for the proportion of all statistics graduate students who plan
to work as university faculty and convert your results to percentages.
A) (21.21%, 32.83%)
B) (19.81%, 35.62%)
C) (22.41%, 35.63%)
D) (20.19%, 36.85%)
E) (20.81%, 35.23%)
19) How much salt does an instant noodle typically have? You take a random sample of 24 instant noodles and
test them in a lab, finding a mean salt content of 1.1 grams and a standard deviation of 0.3 grams of salt.
Create a 95% confidence interval for the mean gram of salt.
A) (0.9800, 1.2200)
B) (0.9943, 1.2267)
C) (0.9708, 1.2292)
D) (0.9733, 1.2267)
E) (0.9368, 1.2632)

20) A 90% confidence interval estimate of the population mean can be interpreted to mean that:
A) If we repeatedly draw samples of the same size from the same population, 90% of the values of the

sample means x will result in a confidence interval that includes the population mean .

A)There is a 90% probability that the population mean
will lie between the lower confidence limit (LCL)
and the upper confidence limit (UCL).
B) We are 90% confident that we have selected a sample whose range of values does not contain the
population mean
.
C) We are 90% confident that 10% the values of the sample means x will result in a confidence interval that

includes the population mean .
E) About 90% of the population fall into this confidence interval.
TRUE/FALSE. Mark ‘A’ if the statement is True and 'B' if the statement is False on your scantron.
21) X ~ Binomial(3, 0.2), then P(X = 1) = 0.384.
A
22) The estimate is the general rule, and the estimator is the specific value from a specific sample.
B
23) The following is a property of a discrete probability distribution: The sum of the probabilities for all the
possible x values equals 1. A
24) The central limit theorem says that the sampling distribution of the sample mean is (approximately) normally
distributed provided the sample size is thirty or larger.
A
25) The practical implication of the effect of a sample proportion on the standard error is: the closer the sample
proportion to .5, the smaller the standard error and thus, the closer the sample proportion tends to fall to the
population proportion.
B
26) The t-distribution is non-symmetric, while the normal distribution is symmetric.
B
27) An estimator is more efficient than another estimator if both are unbiased but the more efficient estimator has
a smaller variance.
A
28) The following is true about t-distribution: It is used to construct confidence intervals for the population mean
when the sample size is small.
A
29) Suppose you have obtained a 90% confidence interval for μ. The relationship between precision and
confidence level is: Increasing the confidence level to 95% will result in greater precision.
B
30) The sample size needed to estimate a population mean within 1.5 units with a 95% confidence when the
population standard deviation equals 10 is at least 171.
A