1. Assume that the data has a normal distribution and the number of observations is greater than fifty.
Find the critical z value used to test a null hypothesis.
Alpha = 0.05 for a two-tailed test. (Points : 5)
±2.575
1.764
±1.96
±1.645
2. Find the value of the test statistic z using z = W4Q3
A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics
include n = 1671 subjects with 30% saying that they play a sport. (Points : 5)
3.38
16.35
-33.38
-16.35
3. Use the given information to find the P-value. Also, use a 0.05 significance level and state the
conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
The test statistic in a right-tailed test is z = 0.52. (Points : 5)
0.6030; fail to reject the null hypothesis
0.3015; fail to reject the null hypothesis
0.3015; reject the null hypothesis
0.0195; reject the null hypothesis
4. Use the given information to find the P-value. Also, use a 0.05 significance level and state the
conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
The test statistic in a two-tailed test is z = -1.63. (Points : 5)
0.1032; fail to reject the null hypothesis
0.0516; reject the null hypothesis
0.0516; fail to reject the null hypothesis
0.9484; fail to reject the null hypothesis
5. Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is
less than 2 in every ten thousand. Assuming that a hypothesis test of the claim has been conducted and
that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
(Points : 5)
There is sufficient evidence to support the claim that the true proportion is less than 2 in ten thousand.
There is sufficient evidence to support the claim that the true proportion is greater than 2 in ten
thousand.
There is not sufficient evidence to support the claim that the true proportion is greater than 2 in ten
thousand.
There is not sufficient evidence to support the claim that the true proportion is less than 2 in ten
thousand.
6. Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error
for the test.
A medical researcher claims that 6% of children suffer from a certain disorder. Identify the type I error
for the test. (Points : 5)
Reject the claim that the percentage of children who suffer from the disorder is different from 6% when
that percentage really is different from 6%.
Reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that
percentage is actually 6%.
Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when
that percentage is actually 6%.
Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when
that percentage is actually different from 6%.
7. Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error
for the test.
A cereal company claims that the mean weight of the cereal in its packets is 14 oz. Identify the type I
error for the test. (Points : 5)
Reject the claim that the mean weight is 14 oz when it is actually greater than 14 oz.
Fail to reject the claim that the mean weight is 14 oz when it is actually different from 14 oz.
Reject the claim that the mean weight is 14 oz when it is actually 14 oz.
Reject the claim that the mean weight is different from 14 oz when it is actually 14 oz.
8. Find the P-value for the indicated hypothesis test.
In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed
to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in
the town that have been exposed to this strain of the flu is 8%. (Points : 5)
0.0048
0.0024
0.0262
0.0524
9. Find the critical value or values of CritValX2 based on the given information.
H0: sigma = 8.0
n = 10
Alpha = 0.01 (Points : 5)
2.088, 21.666
1.735, 23.589
23.209
21.666
10. Find the critical value or values of CritValX2 based on the given information.
H1: sigma < 0.14
n = 23
Alpha = 0.10 (Points : 5)
14.042
14.848
-30.813
30.813
11. Find the number of successes x suggested by the given statement.
Among 660 adults selected randomly from among the residents of one town, 30.2% said that they favor
stronger gun-control laws. (Points : 5)
200
197
199
198
12. Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2, Use
the given sample sizes and numbers of successes to find the pooled estimate p-bar Round your answer
to the nearest thousandth.
n1 = 100; n2 = 100
x1 = 32; x2 = 33 (Points : 5)
0.293
0.227
0.358
0.325
13. Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use
the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test.
n1 = 155; n2 = 146
x1 = 68; x2 = 59 (Points : 5)
z = 7.466
z = 0.435
z = 0.607
z = 13.865
14. Solve the problem.
The table shows the number of pitchers with E.R.A's below 3.5 in a random sample of sixty pitchers from
the National League and in a random sample of fifty-two pitchers from the American League. Assume
that you plan to use a significance level of alpha = 0.05 to test the claim that p1not=p2 Find the critical
value(s) for this hypothesis test. Do the data support the claim that the proportion of National League
pitchers with an E.R.A. below 3.5 differs from the proportion of American League pitchers with an E.R.A.
below 3.5?
W1Q14 (Points : 5)
z = ±1.645; yes
z = 1.645; yes
z = ±2.575; no
z = ±1.96; no
15. Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use
the given sample sizes and numbers of successes to find the P-value for the hypothesis test.
n1 = 100; n2 = 100
x1 = 38; x2 = 40 (Points : 5)
0.0412
0.1610
0.7718
0.2130
16. Construct the indicated confidence interval for the difference between population proportions p1 p2. Assume that the samples are independent and that they have been randomly selected.
x1 = 22, n1 = 38 and x2 = 31, n2 = 52; Construct a 90% confidence interval for the difference between
population proportions p1 - p2. (Points : 5)
0.406 < p1 - p2 < 0.752
-0.190 < p1 - p2 < 0.156
0.373 < p1 - p2 < 0.785
0.785 < p1 - p2 < 0.373
17. Construct the indicated confidence interval for the difference between the two population means.
Assume that the two samples are independent simple random samples selected from normally
distributed populations. Do not assume that the population standard deviations are equal.
Two types of flares are tested and their burning times are recorded. The summary statistics are given
below.
W1Q17
Construct a 95% confidence interval for the differences between the mean burning time of the brand X
flare and the mean burning time of the brand Y flare. (Points : 5)
3.5 min < muX - muY < 5.1 min
3.2 min < muX - muY < 5.4 min
3.6 min < muX - muY < 5.0 min
3.8 min < muX - muY < 4.8 min
18. State what the given confidence interval suggests about the two population means.
A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple
random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were
selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary
statistics are as follows.
W1Q18
The following 98% confidence interval was obtained for mu1 - mu2, the difference between the mean
drying time for paint cans of type A and the mean drying time for paint cans of type B: 4.70hrs < mu1 mu2 < 17.30hrs
What does the confidence interval suggest about the population means? (Points : 5)
The confidence interval includes only positive values which suggests that the two population means
might be equal.
There doesn't appear to be a significant difference between the mean drying time for paint type A and
the mean drying time for paint type B. The modification does not seem to be effective in reducing drying
times.
The confidence interval includes only positive values which suggests that the mean drying time for paint
type A is smaller than the mean drying time for paint type B. The modification does not seem to be
effective in reducing drying times.
The confidence interval includes 0 which suggests that the two population means might be equal. There
doesn't appear to be a significant difference between the mean drying time for paint type A and the
mean drying time for paint type B. The modification does not seem to be effective in reducing drying
times.
The confidence interval includes only positive values which suggests that the mean drying time for
paint type A is greater than the mean drying time for paint type B. The modification seems to be
effective in reducing drying times.
19. Construct the indicated confidence interval for the difference between the two population means.
Assume that the two samples are independent simple random samples selected from normally
distributed populations. Also assume that the population standard deviations are equal (sigma1 =
sigma2), so that the standard error of the difference between means is obtained by pooling the sample
variances.
A researcher was interested in comparing the amount of time spent watching television by women and
by men. Independent simple random samples of 14 women and 17 men were selected and each person
was asked how many hours he or she had watched television during the previous week. The summary
statistics are as follows.
W1Q19
Construct a 95% confidence interval for mu1 - mu2, the difference between the mean amount of time
spent watching television for women and the mean amount of time spent watching television for men.
(Points : 5)
-8.72 hrs < mu1 - mu2 < -2.28 hrs
-8.99 hrs < mu1 - mu2 < -2.01 hrs
-8.18 hrs < mu1 - mu2 < -2.82 hrs
-8.84 hrs < mu1 - mu2 < -2.16 hrs
20. The two data sets are dependent. Find d-bar to the nearest tenth.
W1Q20 (Points : 5)
35.6
21.4
46.3
44.5