STAT 1350, Quiz #14, Summer 2014
Name _______________________________________
1. The name for the pattern of values that a statistic takes when we sample repeatedly from the
same population is
A)
the bias of the statistic.
B)
the sampling distribution of the statistic.
C)
the scale of measurement of the statistic.
D)
the variability of the statistic.
E)
the sampling error.
Ans: B
2. You choose a simple random sample of 100 students at Virginia Commonwealth University
(VCU), and 10 of them own a hybrid vehicle. A 95% confidence interval for the proportion of
all VCU students who own a hybrid vehicle is (approximately)
A)
D)
10  3.
10  6.
B)
E)
0.10  0.03.
0.10  0.06.
C)
0.95  0.0218.
Ans: E
3. A member of the county government thinks that 90% confidence isn’t enough. He wants to be
99% confident. How would the margin of error of a 99% confidence interval based on the
same sample compare with the 90% interval found in the previous question?
A)
It would be smaller because it omits only 1% of the possible samples instead of 10%.
B)
It would be the same because the sample is the same.
C)
It would be larger because higher confidence requires a larger margin of error.
D)
We can’t tell because the margin of error is random.
E)
We can’t tell because it depends on the size of the population.
Ans: C
4. The _______________ says that, as we take more and more observations at random from any
population, the distribution of the mean of these observations eventually gets close to a
Normal distribution.
A)
Statistical inference
C)
Law of large numbers
B)
Normal mean theorem
D)
Central limit theorem
Ans: D
5. If the value of the standardized test statistic is 2.5,
A)
conclude that the null hypothesis and the alternative hypothesis are the same.
B)
we reject the null hypothesis at the 5% significance level.
C)
we fail to reject the null hypothesis at the 5% significance level.
D)
we reject the alternative hypothesis at the 5% significance level.
E)
we should use a different null hypothesis.
Ans: B
6. If a significance test gives P-value 0.005,
A)
the margin of error is 0.005.
B)
the null hypothesis is very likely to be true.
C)
we do not have good evidence against the null hypothesis.
D)
we do have good evidence against the null hypothesis.
E)
the effect of interest is practically significant.
Ans: D
7. The P-value of a test of significance is calculated assuming
A)
the null hypothesis is true.
B)
the alternative hypothesis is true.
C)
nothing—we make no assumptions about which hypothesis is true in order to avoid
bias.
D)
a significance level of 0.05.
Ans: A
8-10. Washington Post columnist Sally Jenkins described an anecdote about golfer Tiger Woods’ ability
to detect subtle differences in golf equipment. Tiger Woods was sent six golf clubs to test. The six clubs
looked identical, but one was heavier than the rest by two grams (about the weight of a dollar bill).
Tiger Woods swung each club and quickly declared, “This one’s heavier.” He was right.
Suppose this basic experiment is carried out for a random sample of 25 professional golfers and five of
them guess the correct club. A statistician carries out a significance test of the null hypothesis that
these golfers were just guessing versus the alternative hypothesis that a greater proportion p of
professional golfers than expected under random chance can recognize the heaviest of six clubs.
8. What are the null and alternative hypotheses in this situation?
A)
H0: p = 1/6
Ha: p > 1/6
B)
H0: p = 0.20
Ha: p > 0.20
C)
H0: p = 0.5
Ha: p > 0.5
D)
H0: p = 0.5
Ha: p ≠ 0.5
Ans: A
9. What is the value of the standardized test statistic for this significance test?
A) 0.417.
B) 0.447.
C) 65.54.
D) 34.46.
Ans: B
10. What is the P-value for this significance test?
A)
less than 0.01
B)
between 0.01 and 0.05
C)
between 0.05 and 0.10
D)
more than 0.10
Ans: D