WorksheetsValid Claims in Statistics
Total questions: 18
Worksheet time: 16mins
Name
Class
Date
1.
Failing to reject a null hypothesis that is false can be characterized as
a)
a Type I error
b)
a Type II error
c)
both a Type I and Type II error
d)
no error
2.
A Type I error is when:
a)
We reject the null hypothesis when it is actually true
b)
We obtain the wrong test statistic
c)
We fail to reject the null hypothesis when it's actually false
d)
We reject the alternate hypothesis when it's actually true
3.
A left-tailed test with n = 41 has a test statistic t = 2.72. Which is the correct p-value?
a)
0.0033
b)
.00486
c)
.0096
d)
Not enough
information
information
4.
A car manufacturer advertises that its new subcompact models get 47 mpg. If μ is the mileage of these cars, what could be the null and alternate hypothesis if we wanted to check if the car's mpg is overrated?
a)
H0 = 47
Ha = 47
Ha = 47
b)
H0 = 47
Ha < 47
Ha < 47
c)
H0 = 47
Ha > 47
Ha > 47
d)
H0 = 47
Ha ≠ 47
Ha ≠ 47
5.
A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?
a)
Ho: μ=21
Ha: μ<21
Ha: μ<21
b)
Ho: p=.20
Ha: p<.20
Ha: p<.20
c)
Ho: p< .21
Ha: p= .21
Ha: p= .21
d)
Ho: p= .21
Ha: p< .21
Ha: p< .21
6.
A P-value indicates:
a)
the probability that the null hypothesis is true
b)
the probability that the alternative hypothesis is true
c)
the probability of obtaining the results (or one more extreme) if the null hypothesis is true
d)
probability of a Type I error
7.
A hypothesis test tests the null hypothesis Ho: μ = 20 against the alternative hypothesis Ha: μ ≠ 20 at a significance level of alpha. If the same procedure is used to test Ho: μ = 20 against Ha: μ > 20 with the same data then the p-value will
a)
increase
b)
decrease
c)
remain the same
d)
be doubled
8.
Which of the following accurately describes the power of a statistical test of hypothesis?
a)
It is equal to the p-value.
b)
It is equal to 1 – (p-value).
c)
It is equal to the significance level.
d)
It is the probability that a test using a fixed value of α will reject H0 when a particular alternative value of the parameter is true.
9.
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 low test statistic
10.
A researcher plans to conduct a test of hypotheses at the α = 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)
0.90
d)
0.99
11.
Which of the following statements is FALSE?
a)
The power of the test increases as α increases.
b)
The power of a test does not depend on the sample size.
c)
The power of a test is the complement of a Type II error.
d)
As the α-level increases, P(Type II error) decreases.
12.
An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect was statistically significant. The explanation is that
a)
new designs typically have more variability than standard designs
b)
the mean of 1200 is large
c)
the new bulbs last longer than the old bulb
d)
the sample size is very large
13.
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.
14.
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.
15.
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.
16.
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
17.
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
18.
H&M is testing a new marketing strategy for increasing sales at its stores. Currently, their stores sell an average of $250,000 per month. Which one of the following sample sizes and significance levels would give their test the most power?
a)
n = 10 with α = 0.01
b)
n = 20 with α = 0.05
c)
n = 40 with α = 0.05
d)
n = 40 with α = 0.10
100 %
