Question 1

If a hypothesis test is to be conducted using  = 0.025, what does that imply about the test?
A) There is a 2.5% chance that the null hypothesis is true.
B) There is a maximum 2.5% chance that a false null hypothesis will be rejected.
C) There is a maximum 2.5% chance that a true null hypothesis will be rejected.
D) There is 2.5% chance of committing a Type I error and 97.5% chance of committing a Type II error.

Accepted Answer

A significance level of 0.025 implies that there is a maximum 2.5% chance that a true null hypothesis will be rejected. This means that if the null hypothesis is actually true, there is only a 2.5% chance that we will incorrectly reject it (and thus incorrectly conclude that the alternative hypothesis is true).

Question 2

What would be the lower limit of a confidence interval, at the 95% level of confidence, for the population proportion if a sample of size 200 had 40 successes?
A) 0.2554
B) 0.2465
C) 0.1535
D) 0.1446

Accepted Answer

The answer of What would be the lower limit of...

Question 3

In testing  vs.  a random sample of size 200 produced a sample proportion  Given these results, what is the approximate p-value of the test?
A) 0.0384
B) 0.0768
C) 0.4616
D) 0.5384

Accepted Answer

The answer of In testing  vs.  a random...

Question 4

Assuming that all necessary conditions are met, what needs to be changed in the formula  so that we can use it to construct a confidence interval estimate for the population proportion p?
A)
B)
C) 
D)

Accepted Answer

The answer of Assuming that all necessary conditions are met,...

Question 5

When testing  vs.  , the observed value of the z-score was found to be -2.15. What would the p-value for this test be?
A) 0.0158
B) 0.0316
C) 0.9684
D) 0.9842

Accepted Answer

The answer of When testing  vs.  , the...

Question 6

If you wish to construct a confidence interval estimate for the difference between two population means, what would an increase in the sample sizes used result in?
A) a decrease in the critical value z
B) a narrower confidence interval
C) a wider confidence interval
D) a confidence interval that contains 0

Accepted Answer

Increasing the sample sizes results in a decrease in the standard error, which makes the confidence interval narrower.

Question 7

Suppose that we reject the null hypothesis  at the 0.05 level of significance. For which of the following  -values do we also reject the null hypothesis?
A) 0.02
B) 0.04
C) 0.06

Accepted Answer

The answer of Suppose that we reject the null hypothesis...

Question 8

In testing  vs.  the test statistic value z is found to be 1.69. What is the p-value of the test?
A) 0.0455
B) 0.0910
C) 0.1977
D) 0.3023

Accepted Answer

The p-value can be found using a standard normal distribution table or calculator. Looking up the value of 1.69 in the table gives a corresponding area of 0.0455. This means that the probability of obtaining a test statistic z at least as extreme as 1.69 is 0.0455. Therefore, the p-value of the test is 0.0455.

Question 9

If you wish to estimate the difference between two population means using two independent large samples, the 90% confidence interval estimate can be constructed using which of the following critical values?
A) 2.33
B) 1.96
C) 1.645
D) 1.28

Accepted Answer

For a 90% confidence interval, the critical value for a standard normal distribution (Z-distribution) is 1.645.

Question 10

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means  . Which of the following best describes the sampling distribution of the sample mean difference  ?
A) It is normally distributed.
B) It is approximately normal.
C) It is student t-distributed with 88 degrees of freedom.
D) It is student t-distributed with 90 degrees of freedom.

Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (typically n > 30). In this case, both sample sizes are greater than 30, so we can assume that the sampling distribution of the sample mean difference will be approximately normal. Therefore, the best choice is B.

Question 11

What is the rejection region for testing at the 0.05 level of significance? A) |z| < 1.28 B) |z| > 1.96 C) z > 1.645 D) z < 2.33

Accepted Answer

To determine the rejection region, we need to find the critical value of the standardized test statistic at the 0.05 level of significance. Since we do not have any information about the population or sample standard deviation, we use the standard normal distribution.

The critical value at the 0.05 level of significance for a two-tailed test is ±1.96. Therefore, the rejection region is |z| > 1.96.

Since we have a two-tailed test, we reject the null hypothesis if the calculated test statistic falls outside this rejection region.

Question 12

In testing the difference between two population means using two independent samples, the population standard deviations were assumed to be known and the calculated test statistic equalled 2.56. If the test was two-tailed and a 5% level of significance had been specified, what would be the most appropriate conclusion from the findings?
A) to reject the null hypothesis
B) not to not reject the null hypothesis
C) to choose two other independent samples
D) to accept the null hypothesis

Accepted Answer

To determine whether to reject or not reject the null hypothesis, we need to compare the calculated test statistic with the critical value from the t-distribution at a 5% level of significance with degrees of freedom calculated based on the sample sizes.
Since this is a two-tailed test, we need to consider both tails of the distribution. At a 5% level of significance, the critical values for this test with degrees of freedom equal to the smaller of the two sample sizes minus 1 is approximately +/- 2.571. Since the calculated test statistic of 2.56 falls inside the range of +/- 2.571, we can reject the null hypothesis and conclude that there is a significant difference between the two population means.

Question 13

If the probability of committing a Type I error for a given test is to be decreased, then for a fixed sample size n, what will happen?
A) The power of the test will increase.
B) The probability of committing a Type II error will increase.
C) The probability of committing a Type II error will decrease.
D) A two-tailed test must be used.

Accepted Answer

Decreasing the probability of a Type I error (alpha) typically increases the probability of a Type II error (beta) if the sample size remains fixed, as there is a trade-off between these two types of errors.

Question 14

When testing  vs.  , the observed value of the z-score was found to be -2.15. Which of the following is the p-value for this test?
A) 0.0158
B) 0.0316
C) 0.9684
D) 0.9842

Accepted Answer

The answer of When testing  vs.  , the...

Question 15

Which of the following conditions must hold before one can make use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p?
A) and) are both greater than 5, wheredenotes the sample proportion
B) np and n(1 - p) are both greater than 5
C) n(p +) and n(p -) are both greater than 5, wheredenotes the sample proportion
D) the sample size is greater than 5

Accepted Answer

The answer of Which of the following conditions must hold...

Question 16

In formulating the null and alternative hypotheses, which of the following would be an acceptable null hypothesis?
A) The population mean is greater than 20.
B) The population mean is smaller than 20.
C) The population mean is equal to 20.
D) The population mean is equal to 0.

Accepted Answer

The null hypothesis always assumes no difference or no effect, so the most acceptable null hypothesis would be that the population mean is equal to a specific value, which in this case is 20. Options A and B suggest there is some difference or effect, making them inappropriate for null hypotheses. Option D suggests a mean of 0, which may not be reasonable or appropriate for the given context.

Question 17

The necessary conditions having been met, a two-tailed test is being conducted to test the difference between two population means, but your statistical software provides only a one-tail area of 0.036 as part of its output. What is the p-value for this test?
A) 0.009
B) 0.018
C) 0.072
D) 0.964

Accepted Answer

The p-value for a two-tailed test is twice the one-tail area. Therefore, 0.036 * 2 = 0.072.

Question 18

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion  , what should we do?
A) take another sample and estimate
B) take two more samples and find the average of their's
C) let= 0.50
D) let= 0.95

Accepted Answer

When there is no knowledge about the approximate values of the sample proportion, the safest option is to assume the worst-case scenario, which is that the sample proportion is 0.5 (or 50%). This will result in the largest possible sample size, which will ensure that the margin of error is kept to a minimum. Therefore, the best choice is to let p= 0.50.

Question 19

When testing  vs.  , the observed value of the z-score was found to be -2.15. What is the p-value for this test?
A) 0.0158
B) 0.0316
C) 0.9684
D) 0.9842

Accepted Answer

Since the z-score is negative, we are interested in finding the area to the left of -2.15 in the standard normal distribution. Using a standard normal table or calculator, we find that the area to the left of -2.15 is approximately 0.0316. This is the p-value for the test, so the best choice is B.

Question 20

In testing  vs.  which of the following would happen if the sample size were increased?
A) The sampling distribution of the sample meanwould have the same variability.
B) There would be no effect on the level of significance for the test.
C) This would have an effect on whether the null hypothesis is true or not.

Accepted Answer

The answer of In testing  vs.  which of...

Quiz 9: A: large-Sample Tests of Hypotheses

If a hypothesis test is to be conducted using = 0.025, what does that imply about the test?

What would be the lower limit of a confidence interval, at the 95% level of confidence, for the population proportion if a sample of size 200 had 40 successes?

In testing vs. a random sample of size 200 produced a sample proportion Given these results, what is the approximate p-value of the test?

Assuming that all necessary conditions are met, what needs to be changed in the formula so that we can use it to construct a confidence interval estimate for the population proportion p? A) B) C) D)

When testing vs. , the observed value of the z-score was found to be -2.15. What would the p-value for this test be?

If you wish to construct a confidence interval estimate for the difference between two population means, what would an increase in the sample sizes used result in?

Suppose that we reject the null hypothesis at the 0.05 level of significance. For which of the following -values do we also reject the null hypothesis?

In testing vs. the test statistic value z is found to be 1.69. What is the p-value of the test?

If you wish to estimate the difference between two population means using two independent large samples, the 90% confidence interval estimate can be constructed using which of the following critical values?

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means . Which of the following best describes the sampling distribution of the sample mean difference ?

What is the rejection region for testing at the 0.05 level of significance?

If the probability of committing a Type I error for a given test is to be decreased, then for a fixed sample size n, what will happen?

When testing vs. , the observed value of the z-score was found to be -2.15. Which of the following is the p-value for this test?

Which of the following conditions must hold before one can make use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p?

In formulating the null and alternative hypotheses, which of the following would be an acceptable null hypothesis?

The necessary conditions having been met, a two-tailed test is being conducted to test the difference between two population means, but your statistical software provides only a one-tail area of 0.036 as part of its output. What is the p-value for this test?

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion , what should we do?

When testing vs. , the observed value of the z-score was found to be -2.15. What is the p-value for this test?

In testing vs. which of the following would happen if the sample size were increased?