Question 1

Under what conditions can the t-distribution be correctly employed to test the difference between two population means?

Accepted Answer

A)  The samples must be small and selected at random from the population. 
B)  The samples must be independent of each other. 
C)  The population variances should be equal or nearly equal, and the populations must be normally distributed. 
D)  All of these. 
E)  None of these. 
A)  The samples must be small and selected at random from the population. 
B)  The samples must be independent of each other. 
C)  The population variances should be equal or nearly equal, and the populations must be normally distributed. 
D)  All of these. 
E)  None of these.

Question 2

With all other factors held constant, confidence intervals constructed with small samples tend to have greater margin of error than those constructed from larger samples.

Accepted Answer

A) True 
 B)False

Question 3

A city bus driver claims that the route from the Canyon Crest Town Center to the University of California, Riverside never varies more than 1.3 minutes. A random sample of 18 trips yielded a variance of 1.26 minutes2. It is of interest to determine if the sample data present sufficient evidence to reject the driver's claim. Calculate the value of the test statistic. What is the appropriate conclusion at the 0.05 level of significance?
Test Statistic = ______________
Reject Region: Reject H0 if   > ______________
Conclusion: ______________
One ______________ conclude that the route varies by more than 1.3 minutes.

Accepted Answer

12.6746; 2

Question 4

In testing the difference between the means of two normally distributed populations, the number of degrees of freedom associated with the unequal-variances t-test statistic usually results in a non-integer number. It is recommended that you:

Accepted Answer

A)  round up to the nearest integer 
B)  round down to the nearest integer 
C)  change the sample sizes until the number of degrees of freedom becomes an integer 
D)  assume that the population variances are equal, and then use df = n1 + n2-2 
E)  assume that the population variances are equal, and then use df = z1 + z2-2 
A)  round up to the nearest integer 
B)  round down to the nearest integer 
C)  change the sample sizes until the number of degrees of freedom becomes an integer 
D)  assume that the population variances are equal, and then use df = n1 + n2-2 
E)  assume that the population variances are equal, and then use df = z1 + z2-2

Question 5

Two independent random samples of sizes   = 4 and   = 5 are selected from each of two normal populations:   Calculate   , the pooled estimator of   .
______________
Find a 90% confidence interval for (   ), the difference between the two population means.
CI = ______________ Enter (n1, n2)
Test   for   = 0.05.
Conclusion:
We ______________ have sufficient evidence to indicate   .

Accepted Answer

12.457; (-

Question 6

Which of the following statements about matched-pairs sampling is correct?

Accepted Answer

A)  It is a procedure that matches each unit from population A with a "twin" from population B so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B. 
B)  It is designed to control for extraneous factors that might influence the characteristic being measured in addition to the variable under study. 
C)  When testing the effectiveness of a new drug compared to a traditional one, each patient in an experimental group might be matched with a partner in a control group of the same age, weight, height, sex, occupation, medical history, lifestyle, and so on. 
D)  All of these. 
E)  None of these. 
A)  It is a procedure that matches each unit from population A with a "twin" from population B so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B. 
B)  It is designed to control for extraneous factors that might influence the characteristic being measured in addition to the variable under study. 
C)  When testing the effectiveness of a new drug compared to a traditional one, each patient in an experimental group might be matched with a partner in a control group of the same age, weight, height, sex, occupation, medical history, lifestyle, and so on. 
D)  All of these. 
E)  None of these.

Question 7

The chi-square distribution is skewed to the left (negatively skewed), but as degrees of freedom increase, it approaches the shape of the binomial distribution.

Accepted Answer

A) True 
 B)False

Question 8

A random sample of size n has been selected from a normally distributed population whose standard deviation is   . In hypothesis testing for the population mean, the t-test should be used instead of the z-test if:

Accepted Answer

A) n > 30 and σ is unknown B) n 30 and σ is unknown and n < 30 and σ is known A) n > 30 and σ is unknown B) n 30 and σ is unknown and n < 30 and σ is known

Question 9

A right-tailed area in the chi-squared distribution equals 0.05. For 8 degrees of freedom the critical value equals 13.362.

Accepted Answer

A) True 
 B)False

Question 10

Which of the following statements is false?

Accepted Answer

A)  The t distribution is symmetric about zero. 
B)  The t distribution is more spread out than the standard normal distribution. 
C)  As the degrees of freedom get smaller, the t distribution's dispersion gets smaller. 
D)  The t distribution is mound-shaped. 
E)  The t distribution is more spread out than the standard normal distribution and as the degrees of freedom get smaller, the t distribution's dispersion gets smaller. 
A)  The t distribution is symmetric about zero. 
B)  The t distribution is more spread out than the standard normal distribution. 
C)  As the degrees of freedom get smaller, the t distribution's dispersion gets smaller. 
D)  The t distribution is mound-shaped. 
E)  The t distribution is more spread out than the standard normal distribution and as the degrees of freedom get smaller, the t distribution's dispersion gets smaller.

Question 11

The following n = 10 observations are a sample from a normal population: 10.4 10.1 9.5 10.5 10.6 9.3 9.9 10.7 9.5 10.0 Find the mean and standard deviation of these data. Find a 99% confidence interval for the population mean   . Test   . Use   = 0.01 Do the results of part (b) support your conclusion in part (c).
Mean = ______________
Standard Deviation = ______________
Test Statistic = ______________
Conclusion: ______________
What is 99% confidence interval? (CI)
CI = ______________ Enter (n1, n2)

Accepted Answer

10.05; .4994; -2.849

Question 12

The symbol   refers to:

Accepted Answer

A)  the difference in the means of two dependent populations 
B)  the difference in the means of two independent populations 
C)  the matched pairs differences 
D)  the mean difference in the pairs of observations taken from two dependent samples 
E)  the mean difference in the pairs of observations taken from two independent samples 
A)  the difference in the means of two dependent populations 
B)  the difference in the means of two independent populations 
C)  the matched pairs differences 
D)  the mean difference in the pairs of observations taken from two dependent samples 
E)  the mean difference in the pairs of observations taken from two independent samples

Question 13

If you are testing   vs.   using a sample of 15 observation and a significance level equal to .05, then the critical value of the test is:

Accepted Answer

A)  1.7613 
B)  6.6450 
C)  23.685 
D)  4.867 
E)  5.319 
A)  1.7613 
B)  6.6450 
C)  23.685 
D)  4.867 
E)  5.319

Question 14

Which of the following statements is true with regard to a hypothesis test for a population variance   ?

Accepted Answer

A)  The null hypothesis is stated in terms of. 
B)  The chi-square distribution is used to determine the critical value. 
C)  The critical value increases as the sample size increases for a given level of significance. 
D)  All of these. 
E)  None of these. 
A)  The null hypothesis is stated in terms of. 
B)  The chi-square distribution is used to determine the critical value. 
C)  The critical value increases as the sample size increases for a given level of significance. 
D)  All of these. 
E)  None of these.

Question 15

If a sample has 15 observations and a 95% confidence estimate for   need to be constructed, the appropriate t-score is 2.131.

Accepted Answer

A) True 
 B)False

Question 16

Which of the following is true about the t distribution?

Accepted Answer

A)  It approaches the normal distribution as its degrees of freedom increase. 
B)  It assumes the population is normally distributed. 
C)  It is more spread out than the standard normal distribution. 
D)  All of these. 
E)  None of these. 
A)  It approaches the normal distribution as its degrees of freedom increase. 
B)  It assumes the population is normally distributed. 
C)  It is more spread out than the standard normal distribution. 
D)  All of these. 
E)  None of these.

Question 17

Two independent samples are selected at random from two normal populations. The sample statistics are as follows:           and   Assume that a two-tailed hypothesis test is conducted at   , what is the critical value?

Accepted Answer

A)  t = 2.0484 
B)  z = 1.96 
C)  t = 1.7011 
D)  z = 1.65 
E)  t = 1.562 
A)  t = 2.0484 
B)  z = 1.96 
C)  t = 1.7011 
D)  z = 1.65 
E)  t = 1.562

Question 18

Which of the following is not a required assumption for constructing a confidence interval estimate of the difference between two population means when the samples are small?

Accepted Answer

A)  The populations are normally distributed. 
B)  The population variances are equal. 
C)  The population variances are equal to 1. 
D)  The samples are selected at random from the populations. 
E)  The population variances are equal and the population variances are equal to 1. 
A)  The populations are normally distributed. 
B)  The population variances are equal. 
C)  The population variances are equal to 1. 
D)  The samples are selected at random from the populations. 
E)  The population variances are equal and the population variances are equal to 1.

Question 19

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit will be:

Accepted Answer

A)  17.110 
B)  6.097 
C)  17.331 
D)  19.353 
E)  11.842 
A)  17.110 
B)  6.097 
C)  17.331 
D)  19.353 
E)  11.842

Question 20

The chi-square distribution can be used in constructing confidence intervals and carrying out hypothesis tests regarding the value of a population variance.

Accepted Answer

A) True 
 B)False

Under what conditions can the t-distribution be correctly employed to test the difference between two population means?

With all other factors held constant, confidence intervals constructed with small samples tend to have greater margin of error than those constructed from larger samples.

In testing the difference between the means of two normally distributed populations, the number of degrees of freedom associated with the unequal-variances t-test statistic usually results in a non-integer number. It is recommended that you:

Which of the following statements about matched-pairs sampling is correct?

The chi-square distribution is skewed to the left (negatively skewed), but as degrees of freedom increase, it approaches the shape of the binomial distribution.

A random sample of size n has been selected from a normally distributed population whose standard deviation is . In hypothesis testing for the population mean, the t-test should be used instead of the z-test if:

A right-tailed area in the chi-squared distribution equals 0.05. For 8 degrees of freedom the critical value equals 13.362.

Which of the following statements is false?

The symbol refers to:

If you are testing vs. using a sample of 15 observation and a significance level equal to .05, then the critical value of the test is:

Which of the following statements is true with regard to a hypothesis test for a population variance ?

If a sample has 15 observations and a 95% confidence estimate for need to be constructed, the appropriate t-score is 2.131.

Which of the following is true about the t distribution?

Two independent samples are selected at random from two normal populations. The sample statistics are as follows: and Assume that a two-tailed hypothesis test is conducted at , what is the critical value?

Which of the following is not a required assumption for constructing a confidence interval estimate of the difference between two population means when the samples are small?

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit will be:

The chi-square distribution can be used in constructing confidence intervals and carrying out hypothesis tests regarding the value of a population variance.

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

The Analysis of Variance

Linear Regression and Correlation

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

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Exam 10: Inference From Small Samples

Under what conditions can the t-distribution be correctly employed to test the difference between two population means?

With all other factors held constant, confidence intervals constructed with small samples tend to have greater margin of error than those constructed from larger samples.

In testing the difference between the means of two normally distributed populations, the number of degrees of freedom associated with the unequal-variances t-test statistic usually results in a non-integer number. It is recommended that you:

Which of the following statements about matched-pairs sampling is correct?

The chi-square distribution is skewed to the left (negatively skewed), but as degrees of freedom increase, it approaches the shape of the binomial distribution.

A random sample of size n has been selected from a normally distributed population whose standard deviation is . In hypothesis testing for the population mean, the t-test should be used instead of the z-test if:

A right-tailed area in the chi-squared distribution equals 0.05. For 8 degrees of freedom the critical value equals 13.362.

Which of the following statements is false?

The symbol refers to:

If you are testing vs. using a sample of 15 observation and a significance level equal to .05, then the critical value of the test is:

Which of the following statements is true with regard to a hypothesis test for a population variance ?

If a sample has 15 observations and a 95% confidence estimate for need to be constructed, the appropriate t-score is 2.131.

Which of the following is true about the t distribution?

Two independent samples are selected at random from two normal populations. The sample statistics are as follows: and Assume that a two-tailed hypothesis test is conducted at , what is the critical value?

Which of the following is not a required assumption for constructing a confidence interval estimate of the difference between two population means when the samples are small?

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit will be:

The chi-square distribution can be used in constructing confidence intervals and carrying out hypothesis tests regarding the value of a population variance.

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

The Analysis of Variance

Linear Regression and Correlation

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

Filters