Question 1

Reducing the probability of a Type I error also reduces the probability of a Type II error.

Accepted Answer

A) True 
 B)False

Question 2

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors' results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:

Accepted Answer

A)  -1.67 
B)  -2.33 
C)  -1.86 
D)  -0.14 
E)  -2.58

Question 3

A new light bulb is being considered for use in an office with computers. It is decided that the new bulb will only be used if it has a mean lifetime of more than 500 hours. A random sample of 40 bulbs is selected and placed on life test. The mean and standard deviation are found to be 505 hours and 18 hours, respectively. Perform the appropriate test of hypothesis to determine whether the new bulb should be used. Use a 0.01 level of significance.
Test statistic = ______________
Critical Value(s) = ______________
Conclusion: ______________
Interpretation: __________________________________________

Accepted Answer

The answer of A new light bulb is being considered...

Question 4

An experiment was conducted to test the effect of a new drug on a viral infection. The infection was induced in 100 mice, and the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection. The second group received the drug. The proportions of survivors,  and  , in the two groups after a 30-day period, were found to be 0.40 and 0.64, respectively. Is there sufficient evidence to indicate that the drug is effective in treating the viral infection? Use  = 0.05.
Test statistic = ______________
Critical Value(s) = ______________
Conclusion: ______________
Interpretation: __________________________________________
Use a 95% confidence interval to estimate the actual difference in the cure rates for the treated versus the control groups.
______________

Accepted Answer

The answer of An experiment was conducted to test the...

Question 5

The test statistic that is used in testing  vs.  is  where  .

Accepted Answer

A) True 
 B)False

Question 6

A one-tailed hypothesis test of the population proportion is used when the alternative hypothesis takes the form  .

Accepted Answer

A) True 
 B)False

Question 7

Which of the following correctly describes hypothesis testing?

Accepted Answer

A)  It is a systematic approach to assessing tentative beliefs about reality. 
B)  It involves confronting beliefs with evidence and deciding, in light of this evidence, whether the beliefs can be maintained as reasonable or must be discarded as untenable. 
C)  It only involves statements about population parameters. 
D)  It is a systematic approach to assessing tentative beliefs about reality and it involves confronting beliefs with evidence and deciding, in light of this evidence, whether the beliefs can be maintained as reasonable or must be discarded as untenable. 
E)  None of these.

Question 8

In testing  vs.  the test statistic value is found to be equal to 1.20. The p-value for this test would be approximately .1151.

Accepted Answer

A) True 
 B)False

Question 9

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means  . The sampling distribution of the sample mean difference  is:

Accepted Answer

A)  normally distributed 
B)  approximately normal 
C)  Student t-distributed with 88 degrees of freedom 
D)  approximately normal and student t-distributed with 88 degrees of freedom 
E)  none of these

Question 10

In a one-tail test about the population proportion p, the p-value is found to be equal to 0.0352. If the test had been two-tail, the p-value would have been 0.0704.

Accepted Answer

A) True 
 B)False

Question 11

In hypothesis testing, the term critical value refers to:

Accepted Answer

A)  the probability, 1 -, of avoiding the Type I error of erroneously rejecting a null hypothesis that is in fact true 
B)  the value of a test statistic that divides all possible values into an acceptance region and a rejection region 
C)  the probability, 1 -, of avoiding the Type O error of erroneously rejecting a null hypothesis that is in fact true 
D)  any sample result that leads to the continued acceptance of the null hypothesis because it has a high probability of occurring when the null hypothesis is true 
E)  the probability, 1 -, of avoiding the Type II error of erroneously accepting a null hypothesis that is in fact false

Question 12

As the significance level  increases, the probability of a Type I error increases and the size of the rejection region increases.

Accepted Answer

A) True 
 B)False

Question 13

A student government representative at a local university claims that 60% of the undergraduate students favor a move to Division I in college football. A random sample of 250 undergraduate students was selected and 140 students indicated they favored a move to Division I.
Perform the appropriate test of hypothesis to test the representative's claim. Use  = 0.05.
Test statistic = ______________
Critical Value(s) = ______________
Conclusion: ______________
Interpretation: __________________________________________
Find the p-value for this test.
p-value = ______________

Accepted Answer

The answer of A student government representative at a local...

Question 14

A two-tailed hypothesis test of the population proportion takes the form  vs.  .

Accepted Answer

A) True 
 B)False

Question 15

Independent random samples of n₁ = 150 and n₂ = 150 sales phone calls for an insurance policy were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 80 successful sales, and sample 2 had 88 successful sales. Suppose you have no preconceived theory concerning which parameter, p₁ or p₂, is the larger and you wish to detect only a difference between the two parameters if one exists. Calculate the standard error of the difference in the two sample proportions, . Make sure to use the pooled estimate for the common value of p. ______________ Calculate the test statistic that you would use for the test above. Based on your knowledge of the standard normal distribution, is this a likely or unlikely observation, assuming that H₀ is true and the two population proportions are the same? Test statistic = ______________ Find the p-value for the test. Test for a significant difference in the population means at the 1% significance level. p-value = ______________ Find the rejection region when = 0.01. Do the data provide sufficient evidence to indicate a difference in the population proportions? Critical Value(s) = ______________ Conclusion: ______________ Interpretation: __________________________________________

Accepted Answer

The answer of Independent random samples of n₁ = 150...

Question 16

A Type II error is committed when we:

Accepted Answer

A)  reject a true null hypothesis 
B)  reject a false null hypothesis 
C)  don't reject a true null hypothesis 
D)  don't reject a false null hypothesis 
E)  do none of these

Question 17

Which of the following statements is (are) not true?

Accepted Answer

A)  The probability of committing a Type I error increases as the probability of committing a Type II error decreases. 
B)  The probability of committing a Type I error and the level of significance are the same. 
C)  The power of the test decreases as the level of significance decreases. 
D)  The probability of committing a Type I error and the level of significance are the same and the power of the test decreases as the level of significance decreases. 
E)  All of these.

Question 18

In order to calculate the p-value associated with a test, it is necessary to know the level of significance  .

Accepted Answer

A) True 
 B)False

Question 19

If you wish to conduct a hypothesis test using a small significance level  , you should have a large sample size to avoid committing a Type II error.

Accepted Answer

A) True 
 B)False

Question 20

If the hypothesis test is conducted using  = .025, this means that:

Accepted Answer

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 
E)  there is a 0.25% chance that the null hypothesis is true

Exam 9: Large-Sample Tests of Hypotheses

Reducing the probability of a Type I error also reduces the probability of a Type II error.

The test statistic that is used in testing vs. is where .

A one-tailed hypothesis test of the population proportion is used when the alternative hypothesis takes the form .

Which of the following correctly describes hypothesis testing?

In testing vs. the test statistic value is found to be equal to 1.20. The p-value for this test would be approximately .1151.

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means . The sampling distribution of the sample mean difference is:

In a one-tail test about the population proportion p, the p-value is found to be equal to 0.0352. If the test had been two-tail, the p-value would have been 0.0704.

In hypothesis testing, the term critical value refers to:

As the significance level increases, the probability of a Type I error increases and the size of the rejection region increases.

A two-tailed hypothesis test of the population proportion takes the form vs. .

A Type II error is committed when we:

Which of the following statements is (are) not true?

In order to calculate the p-value associated with a test, it is necessary to know the level of significance .

If you wish to conduct a hypothesis test using a small significance level , you should have a large sample size to avoid committing a Type II error.

If the hypothesis test is conducted using = .025, this means that: