15 MCQs In Statistics
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.
a = 0.05 for a twotailed test. (Points : 5)
±2.575
1.764
±1.96
±1.645
2. Find the value of the test statistic z using z =
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 Pvalue. 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 righttailed 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 Pvalue. 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 twotailed 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 Pvalue 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 Pvalue 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
based on the given information.
H0:
σ = 8.0
n = 10
= 0.01 (Points : 5)
2.088, 21.666
1.735, 23.589
23.209
21.666
10. Find the critical value or values of
based on the given information.
H1:
< 0.14
n = 23
= 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 guncontrol 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
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. 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 Pvalue for the hypothesis test.
n1 = 100; n2 = 100
x1 = 38; x2 = 40 (Points : 5)
0.0412
0.1610
0.7718
0.2130
15. 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

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