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   two-tailed 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 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

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 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

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   P-value 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