ELEMENTARY STATISTICS EXAM 3
COMPREHENSIVE REVIEW SHEET
VERIFIED QUESTION BANK
●● Which of the following is a common limitation of hypothesis
testing?
Answer: Both a and b: Conclusions are made about the data set rather
than about the hypothesis itself; Demonstrating a significant treatment
effect does not necessarily indicate a substantial treatment effect.
●● A research report summarizes the results of the hypothesis test by
stating, "z = 3.11, p < .01." Which of the following is a correct
interpretation of this report?
Answer: The null hypothesis was rejected, and the probability of a Type
I error is less than .01.
●● What would be the result of setting an alpha level extremely small?
Answer: Both a and b: There would be almost no risk of a Type I error;
It would be very difficult to reject the null hypothesis.
●● Assuming a normal distribution, which of the following would call
for a one-tailed hypothesis test rather than a two-tailed test?
Answer: Determining if driving a red car increases the number of
speeding tickets per year
,●● If other factors are held constant, then how does the sample size
affect the likelihood of rejecting the null hypothesis and the value for
Cohen's d?
Answer: A larger sample size increases the likelihood of rejecting the
null hypothesis but does not change the value of Cohen's d.
●● Which of the following correctly describes the effect that decreasing
sample size and decreasing the standard deviation have on the power of
a hypothesis test?
Answer: A decrease in sample size will decrease the power, but a
decrease in standard deviation will increase the power.
●● What is the primary concern when selecting an alpha value?
Answer: To minimize Type I errors
●● What is a Type I error?
Answer: When a researcher rejects a null hypothesis that is actually true.
●● Which of the following are correct ways of defining the power of a
statistical test?
I. The probability that the test will correctly reject a false null hypothesis
II. The probability that the test will result in a Type II error
III. The probability that the test will not result in a Type II error
,Answer: I and III only
●● A random sample is normally distributed. If all values in the sample
and all values in the population are multiplied by 2, what is the impact
on Cohen's d?
Answer: Stays the same
●● Which of the following explains why it is easier to reject the null
hypothesis with a one-tailed test than with a two-tailed test with all the
same parameters?
Answer: Because the critical region is all on one side in a one-tailed test
and needs to be split between the two tails in a two-tailed test
●● A treatment is administered to a sample selected from a population
with a mean of μ = 40 and a standard deviation of σ = 6.25. After
treatment, the sample mean is M = 45. Based on this information, the
effect size as measured by Cohen's d can be classified as which of the
following?
Answer: Large effect
●● A researcher expects a treatment to produce a decrease in the
population mean. The treatment is evaluated using a one-tailed
hypothesis test. Which z-scores would lead us to reject the null
hypothesis with α = .05?
I. z = -1.75
, II. z = 1.75
III. z = -1.6
IV. z = 1.6
Answer: 1 only
●● In a normal sample distribution with n = 16, the null hypothesis is
rejected. If the sample size is changed to 64 with all other factors staying
the same, what happens to the z-score and the decision about the null
hypothesis?
Answer: The z-score is doubled, and the null hypothesis is still rejected.
●● A random sample is selected from a normal population with a mean
of μ = 200 and a standard deviation of σ = 12. After a treatment is
administered to the individuals in the sample, the sample mean is found
to be M = 196. How large a sample is necessary for this sample mean to
be statistically significant using a two-tailed test with α = .05?
Answer: 35
●● A study is conducted to see if teenagers drive at faster average speeds
than the general population of drivers. The average speed of the driving
population is 35 mph. The null hypothesis is H0: μaverage driving speed
of teenagers = 35 mph. What is the alternative hypothesis?
Answer: H1: μdriving speed of teenagers ≠ 35 mph
COMPREHENSIVE REVIEW SHEET
VERIFIED QUESTION BANK
●● Which of the following is a common limitation of hypothesis
testing?
Answer: Both a and b: Conclusions are made about the data set rather
than about the hypothesis itself; Demonstrating a significant treatment
effect does not necessarily indicate a substantial treatment effect.
●● A research report summarizes the results of the hypothesis test by
stating, "z = 3.11, p < .01." Which of the following is a correct
interpretation of this report?
Answer: The null hypothesis was rejected, and the probability of a Type
I error is less than .01.
●● What would be the result of setting an alpha level extremely small?
Answer: Both a and b: There would be almost no risk of a Type I error;
It would be very difficult to reject the null hypothesis.
●● Assuming a normal distribution, which of the following would call
for a one-tailed hypothesis test rather than a two-tailed test?
Answer: Determining if driving a red car increases the number of
speeding tickets per year
,●● If other factors are held constant, then how does the sample size
affect the likelihood of rejecting the null hypothesis and the value for
Cohen's d?
Answer: A larger sample size increases the likelihood of rejecting the
null hypothesis but does not change the value of Cohen's d.
●● Which of the following correctly describes the effect that decreasing
sample size and decreasing the standard deviation have on the power of
a hypothesis test?
Answer: A decrease in sample size will decrease the power, but a
decrease in standard deviation will increase the power.
●● What is the primary concern when selecting an alpha value?
Answer: To minimize Type I errors
●● What is a Type I error?
Answer: When a researcher rejects a null hypothesis that is actually true.
●● Which of the following are correct ways of defining the power of a
statistical test?
I. The probability that the test will correctly reject a false null hypothesis
II. The probability that the test will result in a Type II error
III. The probability that the test will not result in a Type II error
,Answer: I and III only
●● A random sample is normally distributed. If all values in the sample
and all values in the population are multiplied by 2, what is the impact
on Cohen's d?
Answer: Stays the same
●● Which of the following explains why it is easier to reject the null
hypothesis with a one-tailed test than with a two-tailed test with all the
same parameters?
Answer: Because the critical region is all on one side in a one-tailed test
and needs to be split between the two tails in a two-tailed test
●● A treatment is administered to a sample selected from a population
with a mean of μ = 40 and a standard deviation of σ = 6.25. After
treatment, the sample mean is M = 45. Based on this information, the
effect size as measured by Cohen's d can be classified as which of the
following?
Answer: Large effect
●● A researcher expects a treatment to produce a decrease in the
population mean. The treatment is evaluated using a one-tailed
hypothesis test. Which z-scores would lead us to reject the null
hypothesis with α = .05?
I. z = -1.75
, II. z = 1.75
III. z = -1.6
IV. z = 1.6
Answer: 1 only
●● In a normal sample distribution with n = 16, the null hypothesis is
rejected. If the sample size is changed to 64 with all other factors staying
the same, what happens to the z-score and the decision about the null
hypothesis?
Answer: The z-score is doubled, and the null hypothesis is still rejected.
●● A random sample is selected from a normal population with a mean
of μ = 200 and a standard deviation of σ = 12. After a treatment is
administered to the individuals in the sample, the sample mean is found
to be M = 196. How large a sample is necessary for this sample mean to
be statistically significant using a two-tailed test with α = .05?
Answer: 35
●● A study is conducted to see if teenagers drive at faster average speeds
than the general population of drivers. The average speed of the driving
population is 35 mph. The null hypothesis is H0: μaverage driving speed
of teenagers = 35 mph. What is the alternative hypothesis?
Answer: H1: μdriving speed of teenagers ≠ 35 mph
