WorksheetsChapter 9 The Practice of Statistics AP Stats
Total questions: 24
Worksheet time: 32mins
Name
Class
Date
1.
To determine if having children within the first two years of marriage increases the divorce rate, where p = proportion of marriages that end in divorce, we should test the hypotheses
a)
Ho: p̂ = 0.5; Ha: p̂ ≠ 0.5
b)
Ho: p̂ = 0.5; Ha: p̂ > 0.5
c)
Ho: p > 0.5; Ha: p = 0.5
d)
Ho: p = 0.5; Ha: p > 0.5
2.
In their advertisements, a new diet program would like to claim that their methods result in a mean weight loss of more than ten pounds in two weeks. In order to determine if this is a valid claim, they hire an independent testing agency that then selects twenty-five people to be placed on this diet. The agency should be testing the null hypothesis H0: m = 10 and the alternative hypothesis
a)
Ha: μ < 10
b)
Ha: μ > 10
c)
Ha: μ ≥ 10
d)
Ha: μ ≤ 10
3.
The average growth of a certain variety of pine tree is 10.1 inches in three years. A biologist claims that a new variety will have a greater three-year growth. A random sample of 25 of the new variety has an average three-year growth of 10.8 inches and a standard deviation of 2.1 inches. The appropriate null and alternative hypotheses to test the biologist's claim are
a)
H0: µ = 10.8 against Ha: µ > 10.8
b)
H0: µ = 10.8 against Ha: µ 10.8
c)
H0: µ = 10.1 against Ha: µ > 10.1
d)
H0: µ = 10.1 against Ha: µ < 10.1
4.
The P-value of a test of a null hypothesis is the probability that
a)
assuming the null hypothesis is true, the test statistic will take a value at least as extreme as that actually observed.
b)
assuming the null hypothesis is false, the test statistic will take a value at least as extreme as that actually observed.
c)
the null hypothesis is true.
d)
the null hypothesis is false.
5.
In testing hypotheses, which of the following would be strong evidence against the null hypothesis?
a)
Using a small level of significance
b)
Using a large level of significance
c)
Obtaining data with a small P-value
d)
Obtaining data with a large P-value
6.
I conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level a = 0.05. I may conclude that
a)
the test would also be significant at level a = 0.10.
b)
the test would also be significant at level a = 0.01.
c)
the P-value is less than .05.
d)
both (A) and (C) are true.
7.
A test of significance produces a P-value of 0.024. Which of the following conclusions is appropriate?
a)
Accept Ha at the α = 0.05 level
b)
Reject Ha at the α = 0.01 level
c)
Fail to reject H0 at the α = .05 level
d)
Reject H0 at the α = 0.05 level
8.
If we reject the null hypothesis when, in fact, it is true, we have
a)
committed a Type I error.
b)
committed a Type II error.
c)
a probability of being correct that is equal to the P-value.
d)
a probability of being correct that is equal to 1 – P-value.
9.
A Type II error is
a)
rejecting the null hypothesis when it is true.
b)
failing to reject the null hypothesis when it is false.
c)
incorrectly specifying the null hypothesis.
d)
incorrectly specifying the alternative hypothesis.
10.
A researcher plans to conduct a test of hypotheses at the a = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type I error is
a)
0.01
b)
0.10
c)
0.89
d)
0.90
11.
A researcher plans to conduct a test of hypotheses at the a = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which she computed the power is
a)
0.01
b)
0.10
c)
0.89
d)
0.90
12.
In testing hypotheses, if the consequences of incorrectly rejecting the null hypothesis are very serious, we should
a)
use a very large level of significance.
b)
use a very small level of significance.
c)
insist that the P-value be smaller than the level of significance.
d)
insist that the level of significance be smaller than the P-value.
13.
The power of a statistical test of hypotheses is
a)
the smallest significance level at which the data will allow you to reject the null hypothesis.
b)
equal to 1 - (P-value).
c)
the probability that the test will reject both one-sided and two-sided hypotheses.
d)
the probability that a significance test will reject the null hypothesis when a particular alternative value of the parameter is true.
14.
Which of the following will increase the power of a statistical test of significance
a)
Increase the Type II error probability
b)
Increase the sample size
c)
Decrease the α level
d)
All of the above
15.
Which of the following statements is FALSE?
a)
The power of a hypothesis test increases as a increases.
b)
The power of a hypothesis test does not depend on the sample size.
c)
The power of a test is the complement of the probability of a Type II error.
d)
The power of a hypothesis test is a measure of the ability of the test to detect a difference between the estimated value and the true value of a parameter.
16.
In hypothesis testing, β is the probability of committing a Type II error. The power of the test, 1 - β, is then
a)
the probability of rejecting H0 when Ha is true.
b)
the probability of failing to reject H0 when Ha is true.
c)
the probability of failing to reject H0 when H0 is true.
d)
the probability of rejecting H0 when H0 is true.
17.
An advertiser wishes to see if a new advertisement is effective in promoting an existing product. The previous advertisement has a recognition score of 3.7. An SRS of 12 potential buyers resulted in a mean recognition score of 3.4 with a standard deviation of 1.7. Which of the following required conditions for conducting a t-test for a mean has not been met?
a)
The population is at least 10 times the sample size.
b)
The data are taken from a simple random sample.
c)
The population is Normally distributed or n is large.
d)
The decision of each buyer is independent.
18.
Your teacher claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you’ve been keeping track. In the past 80 rolls, the number “five” has come up only 8 times. You suspect that the calculator is producing fewer fives than it should. Let p = actual long-run proportion of five’s produced by the calculator. The hypotheses for testing the teacher's claim are:
a)
H0: p = 0.2; Ha: p ≠ 0.2
b)
H0: p = 0.2; Ha: p > 0.2
c)
H0: p = 0.2; Ha: p < 0.2
d)
H0: p̂ = 0.1; Ha: p̂ < 0.1
19.
Your teacher claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you’ve been keeping track. In the past 80 rolls, the number “five” has come up only 8 times. You suspect that the calculator is producing fewer fives than it should. Let p = actual long-run proportion of five’s produced by the calculator. The P-value for this test is closest to:
a)
-2.24
b)
0.0014
c)
0.0028
d)
0.0125
20.
An SRS of 100 postal employees found that the average time these employees had worked for the postal service was J = 7 years with standard deviation s = 2 years. Assume the distribution of the time the population of employees have worked for the postal service is approximately Normal with mean m. Are these data evidence that m has changed from the value of 7.5 years of 20 years ago? To make this determination we test the hypotheses H0: m = 7.5, Ha: m 7.5 using a one-sample t test. Which of the following intervals contains the P-value or this test?
a)
larger than 0.1
b)
between 0.1 and 0.05
c)
between 0.05 and 0.01
d)
below 0.01
21.
You construct a 95% confidence interval for a mean and find it to be 1.1 ± 0.8. Which of the following is true?
a)
A test of the hypotheses H0: μ = 1.2, Ha: μ ≠ 1.2 would reject H0 at the 0.05 level.
b)
A test of the hypotheses H0: μ = 1.1, Ha: μ ≠ 1.1 would reject H0 at the 0.05 level
c)
A test of the hypotheses H0: μ = 0, Ha: μ ≠ 0 would reject H0 at the 0.05 level
d)
All three tests above would reject H0 at the 0.05 level.
22.
Nine swimmers are randomly selected from a large group. Each is asked to hold their breath for as long as possible and the times are recorded. Then they are given instructions in a new method for relaxing while holding their breath. Afterwards, they are again timed on how long they can hold their breath. We wish to perform a t-test on this paired data to see if the swimmers held their breath for longer after receiving breath-holding instructions. Which of the following is not a required condition to perform a t-test on these paired data?
a)
We must be able to view these swimmers as a SRS of all swimmers who might receive this training.
b)
The distribution of the swimmers breath-holding times before the training is approximately Normal.
c)
Each swimmer’s gain in breath-holding time is independent of the other swimmers.
d)
The distribution of gains in breath-holding times of the swimmers is approximately Normal.
23.
A student’s AP statistics project involves comparing the time it takes a student to complete a set of 25 basic trinomial factoring problems while listening to either rap music or country music. Twelve students are timed on two different sets of problems and the order of both which set of problems he does first and which music he listens to first are randomized. The resulting data is thus paired, with each student acting as his own “pair.” Which of the following conditions is required to perform a t-test on these paired data?
a)
The distribution of times for all students on each set of problems must be approximately Normal.
b)
The distribution of times for all students while listening to each type of music must be approximately Normal.
c)
The distribution of times for all 24 sets of problems (12 students are taking 2 tests each) must be approximately Normal.
d)
The distribution of differences between each individual student’s times on each of the two tests (time with rap – time with country) must be approximately Normal.
24.
You have data on rainwater collected at 16 locations in the Adirondack Mountains of New York State. One measurement is the acidity of the water, measured by pH on a scale of 0 to 14 (the pH of distilled water is 7.0). Which inference procedure would you use to estimate the average acidity of rainwater in the Adirondacks?
a)
one-sample z interval for μ
b)
one-sample t interval for μ
c)
one-proportion z-test
d)
one-sample t test
100 %
