Statistics 13A Summer Session II, 2009
Sample Midterm 3
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) A researcher claims that 62% of voters favor gun control. Determine the null and alternative hypotheses.
A) Ho: p ≠ 0.62 vs. Ha: p = 0.62
B) Ho: p ≥ 0.62 vs. Ha: p < 0.62
C) Ho: p = 0.62 vs. Ha: p ≥ 0.62
D) Ho: p < 0.62 vs. Ha: p ≥ 0.62
E) Ho: p = 0.62 vs. Ha: p ≠ 0.62
2) In a sample of 150 children selected randomly from one town, it is found that 24 of them suffer from asthma. Find the
P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.
(the alternative is right-tailed).
A) 0.05
B) 0.95
C) 0.01
D) 0.025
E) 0.975
3) Test the claim that for the population of female college students, the mean weight is given by  = 132 lb. Sample data
are summarized as n = 20, x = 137 lb, and s = 14.2 lb. Find the test statistic.
A) 1.729
B)20
C) 1.57
D)14.2
E)-1.57
4) Failing to reject a false Ho:
A) is a Type I error.
B) has probability 1 - β of occurring.
D) has probability α of occurring.
E) is a correct decision
C) is a Type II error.
5) At one school, the average amount of time that ninth-graders spend watching television each week is 21.6 hours. The
principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants
to perform a significance test to determine whether the average amount of time spent watching television per week
has decreased from the previous mean of 21.6 hours. Which type of the significance test should be used?
A) Left-tailed
B) Right-tailed
C)Middle-tailed
D) Two-tailed
E) Neither
6) 410 people were asked if they were satisfied with their jobs. 37% said they were. It is wished to test the following null
hypothesis: Ho: p = 0.3. Find the test statistic.
A) 4.125
B) 0.037
C) 0.153
D) 2.612
E) 3.093
7) Given Ha: p ≠ p0. What is the P-value if the test statistics is calculated to be z = 1.08?
A) 0.28
B) 0.58
C) 0.11
D) 0.05
E) 0.22
8) An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims
that the figure is higher for fathers in the town of Cheraw. A random sample of 233 fathers from Cheraw yielded 96
who did not help with child care. Do the data provide sufficient evidence to conclude that in Littleton the proportion
is higher than 0.34? Use a 0.05 significance level.
Ho: p = 0.34, Ha: p > 0.34; α = 0.05. Test statistic: z = 2.32. P-Value = 0.0102. State your conclusion in terms of the
null hypothesis.
A) Do not reject Ho.
B) Do not reject Ha.
C) Reject H0.34.
D) Reject Ho.
E) Accept Ho.
9) From the statistics given below, find the value of the point estimate for the difference in proportions
n1 = 216, x1 = 76, n2 = 186, x2 = 99
A) 0.392
B) 0.180
C) 0.435
D) 0.308
E) 0.218
10) The U.S. Department of Labor and Statistics wanted to compare the results of an unemployment program for the past
two months in the U.S. Suppose the proportion of the unemployed two months ago is p2 and the proportion of the
unemployed one month ago is p1. A study found a 99% confidence interval for p2 – p1 is (-0.0012, 0.003). Give an
interpretation of this confidence interval.
A) We are 99% confident that the proportion of the unemployed one month ago is between 0.12% less and 0.3%
more than the proportion of the unemployed two months ago.
B) We are 99% confident that the proportion of the unemployed two months ago is between 0.12% less and 0.3%
more than the proportion of the unemployed one month ago.
C) We know that 99% of the unemployed two months ago is between 0.12% less and 0.3% more than the
unemployed one month ago.
D) We know that 99% of all random samples done on the population will show that the proportion of the
unemployed two months ago is between 0.12% less and 0.3% more than the proportion of the unemployed
one month ago.
E) We know that 99% of the unemployed one month ago is between 0.12% less and 0.3% more than the
unemployed two months ago.
11) A two-sided significance test for two population proportions is to be performed using the P-value approach.
Ho: p1 - p2 = 0, Ha: p1 - p2 ≠ 0 . Use the given sample data to find the P-value for the significance test. Give an
interpretation of the P-value. n1 = 200, p̂1 = 0.10, n2 = 200, p̂2 = 0.08.
A) P-value = 0.2119; If there is no difference in the proportions, there is about a 21.19% chance of seeing the
observed difference or larger by natural sampling variation.
B) P-value = 0.4840; There is about a 48.40% chance that the two proportions are equal.
C) P-value = 0.4840; If there is a difference in the proportions, there is a 48.40% chance of seeing the observed
difference by natural sampling variation.
D) P-value = 0.4840; If there is no difference in the proportions, there is about a 48.40% chance of seeing the
observed difference or larger by natural sampling variation.
E) P-value = 0.2119; There is about a 21.19% chance that the two proportions are equal
12) A researcher is interested in the academic performance differences between individuals using an optimistic versus a
pessimistic approach to their studies. If the researcher fails to find a significant difference, when in fact one exists in
the population:
A) the null hypothesis was correctly accepted.
B) the null hypothesis was correctly rejected.
C) the research hypothesis was correctly accepted.
D) a Type 2 error has been made.
E) a Type 1 error has been made.
13) A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by
following a particular diet. Use the sample data below to construct a 99% confidence interval for 1 - 2 where 1 and
2 represent the means for the treatment group and the control group respectively.
Treatment Group: n = 85, x = 189.1, s = 38.7
Control Group:
n = 75, x = 203.7, s = 39.2
A) (-30.5, 1.3)
B) (-29.0, -0.2)
C)(-1.3, 30.5)
D) (-1.5, 30.7)
E) (-26.8, -2.4)
14) Refer to Problem 13. Assume that the assumptions and conditions for inference with a two-sample t-test are met. Test
the claim that the treatment population mean 1 is smaller than the control population mean 2. Test the claim using a
significance level of 0.01. State your conclusion.
A) Reject Ho.
B) Reject Ha.
C) Do not reject Ho.
D) Do not reject Ha.
E) The control group should be changed.
15) One hundred sixty students who were majoring in either math or English were asked a test question. The researcher
recorded whether they answered the question correctly. The response and the major are independent. The results are
shown in the table.
Accuracy
Proportion
Calculate the 98% confidence interval for (pmath – pEnglish )
A) (.352, .463)
B) (-.703,-.352)
C) (-.379, -.021) D) (.503, .708)
E) (-.323, -.077)
16) The central limit theorem states that the sampling distribution of x1 – x2 is (approximately) normal.
A) when at least one of the sample sizes is greater than or equal to 30.
B) when the total number sampled is greater than or equal to 30.
C) when either one of the sample sizes is greater than or equal to 30.
D) regardless of both of the sample sizes.
E) when both of the sample sizes are greater than or equal to 30.
17) Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four tosses. What are the
possible values of the random variable X?
A) 1, 2, 3, 4
B) 0, 1, 2, 3
C) 1, 2, 3, 4, 5
D) 0, 1, 2, 3, 4
E) 0, 1, 2, 3, 4, 5
18) Refer to problem 17. Find the probability distribution of the random variable X.
A) P(X=0)=1/16
P(X=1)=1/4 P( X=2)=3/8
P(X=3)=1/4
P(X=4)=1/16
B) P(X=1)=1/16
P(X=2)=1/4 P( X=3)=3/8
P(X=4)=1/4
P(X=5)=1/16
C) P(X=0)=1/4
P(X=1)=1/4
P( X=2)=1/2
P(X=3)=1/4
P(X=4)=1/4
D) P(X=1)=1/16
P(X=2)=3/8 P( X=3)=3/8
P(X=4)=1/16
E)
P(X=0)=1/16
P(X=1)=3/8 P( X=2)=3/8
P(X=3)=1/16
19) Doctors estimate that 53% of college students go to bed before midnight. If they survey 5 students at random, find the
probability that at most 4 of them are going to bed before midnight.
A) 0.958
B) 0.0418
C) 0.460
D) 0.185
E) 0.975
20) In a poll of 278 voters in a certain city, 67% said that they backed a bill which would limit growth and development
in their city. The margin of error in the poll was reported as 5.5 percentage points (rounded, 95% confidence level,
z=1.96). Which statement is correct?
A) The reported margin of error is consistent with the sample size.
B) There is not enough information to determine the margin of error.
C) For the given sample size, the margin of error should be much larger than stated.
D) The sample size is too small to achieve a margin of error less than 10%.
E) For the given sample size, the margin of error should be much smaller than stated.
21) 350 randomly selected students took the statistics final. If the margin of error for a 99% confidence interval is 4.45,
and the sample mean is 86 (with the standard deviation 12.2), identify the correct lower limit of a 98% confidence
interval for the mean score of all students.
A) 84.32
B) 89.2
C) 84.48
D) 73.86
E) 83.98
22) Find the standard deviation for the number of people who like to drive fast for a group of n=29, if it is known that the
probability is 0.48 that a randomly selected person says that he/she likes to drive fast.
A) 13.92
B) 7.2384
C) 3.24
D) 2.690
E) 0.093
23) Assume that the weights of newborn babies are normally distributed with a mean of 6 pounds and a standard
deviation of 1.2 pounds. If 20 newborn babies are randomly selected from this population, find the z-score of an
average weight of x = 6.7 pounds.
A) -1.667
B) 2.608
C) 2.61
D) 0.58
E) -2.33
24) Which of the following is a property of the correlation coefficient, r?
A) The closer r is to zero, the weaker the linear relationship between x and y.
B) r measures the strength of any kind of relationship between x and y.
C) r depends on which variable is treated as the response variable.
D) r is always between 0 and 1.
E) r depends on the units of y or x.
25) Let a sample consist of the following observations: 0.9 0.8 0.1 0.2 0.3 0.5 0.3. Find the mean value.
A) 0.3875
B) 0.30
C) 3.1
D) 0.443
E) 0.043
26) The expression P(A ∩ B) = P(A)P(B|A) is valid if
A) A and B are dependent.
B) A and B are independent.
C) for any events A and B.
D) only if A equals BC.
E) A and B are mutually exclusive.
27) The following results were obtained from a regression; ŷ = 5 – 6.2x, r = 0.92, Sx = 4, Sy= 30, y = 13, Find x .
A) 14.24
B) 13.8
C) -1.29
D) 0.23
E) 5.43
28) If the sample consists of observations: 2 2 3 4 5 5, which of the following will change if observation ‘2’ is changed
to ‘4’?
A) Mode
B) Median
C) Mean
D) Variance
E) All of above
29) Probability that a girl learns to read by the age of 3 is 0.78. Probability that a girl learns to read by the age of 4 is 0.34.
If a second child is born into a family, what is the probability that this child will learn to read by age of 4 and is a girl?
A) 0.68
B) 0.39
C) 0.17
D) 0.085
E) 0.34
30) The table below describes the anxiety level of freshman in high school.
High
Medium
Low
Total
Men
121
53
22
196
Women
152
98
12
262
Total
273
151
34
458
What is the probability that a freshman in high school has medium anxiety?
A) 0.116
B) 0.214
C) 0.596
D) 0.074
E) 0.330
TRUE/FALSE. Mark ‘A’ if the statement is True and 'B' if the statement is False on your scantron.
31) If p-value of the test statistic is smaller than , conclude ‘Reject Ho’. TRUE
32) For a given level of significance, increasing the sample size will always decrease the probability of committing a Type
I error. FALSE
33) The actual P-value is less informative than reporting the result of the test as “Reject Ho” versus “Do Not Reject Ho”.
FALSE
34) If the P-value of the test statistic was found to be 0.9 for testing Ho: p = 0.8 against Ha: p < 0.8, then the correct
conclusion is ‘there is strong evidence that p < 0.8’. FALSE
35) The goal of the hypothesis test is to prove the null hypothesis. FALSE
36) A hypothesis test is significant when the P-value is greater than β (=P(type II error). FALSE
37) When the confidence intervals for 1 – 2 contains zero, it is possible to predict which population mean is equal to
zero. FALSE
38) However small the difference between two population proportions, for sufficiently large sample sizes, the null
hypothesis of equal population proportions is likely to be rejected. TRUE
39) If a test rejects Ho: 1 = 2, then the confidence interval for (1 – 2) having the same error probability does not
contain zero. TRUE
40) For two estimates from independent samples, the standard error is
FALSE
41) X is distributed as a Binomial(n=7, p=0.52), then P(X = 3.4) = 0. TRUE
42) A point estimate alone is less informative because it tells us how close the estimate is likely to be
to the parameter. FALSE
43) A probability distribution specifies the possible probabilities for the outcome values of a random variable. TRUE
44) The normal distribution it is symmetric, whereas t-distribution is not because it depends on the degrees of freedom.
FALSE
45) Suppose you have obtained a 95% confidence interval for μ. The relationship between precision and confidence level
is: Decreasing the sample size will result in a wider confidence interval but will not change the confidence level.
TRUE
46) To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day. This technique
produces a random sample. FALSE
47) As long as the sample size is large, random sample always will be produced.
FALSE
48) A group of volunteers for a clinical trial consists of 88 women and 80 men. 22 of the women and 20 of the men have
high blood pressure. High blood pressure and gender are independent. TRUE
49) The binomial distribution requires at least one success.
50) Disjoint events are independent events. FALSE
FALSE