Question 1

Regardless of the degrees of freedom, every t-distribution is symmetric around zero.

Accepted Answer

A) True 
 B)False

Question 2

A random sample of size 25 taken from a normally distributed population resulted in a sample standard deviation of a 0.93054. The lower and upper limits of a 99% confidence interval for the population variance would be:

Accepted Answer

A)  9.886 and 45.559 
B)  3.144 and 6.750 
C)  0.678 and 1.449 
D)  0.456 and 2.102 
E)  1.493 and 6.430

Question 3

Statisticians have shown that for given sample sizes  and  , the number of degrees of freedom associated with the equal-variances test statistic and confidence interval estimator of  is always greater than or equal to number of degrees of freedom associated with the unequal-variances test statistic and confidence interval estimator.

Accepted Answer

A) True 
 B)False

Question 4

The chi-squared distribution is:

Accepted Answer

A)  symmetric around zero 
B)  positively skewed 
C)  negatively skewed 
D)  mound-shaped 
E)  positively skewed and mound-shaped

Question 5

Two different brands of contact lenses are to be compared for length, in hours, of comfortable wear. The lenses are available in any prescription.
How might an experiment resulting in paired data be carried out?
________________________________________________________
How might an independent samples experiment be carried out?
________________________________________________________
Which method would you recommend, and why?
________________________________________________________

Accepted Answer

The answer of Two different brands of contact lenses are...

Question 6

Researchers determined that 60 Kleenex tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52 and s = 22. Suppose the test statistic does fall in the rejection region at  = 0.05. Which of the following conclusions is correct?

Accepted Answer

A)  At= 0.05, we do not reject 
B)  At= 0.05, we reject 
C)  At= 0.05, we accept 
D)  At= 0.10, we do not reject 
E)  none of these

Question 7

If a sample of size 20 is randomly selected from a population, the value of A for the probability P(-A  t  A) = 0.95 is 2.093.

Accepted Answer

A) True 
 B)False

Question 8

Thirty-five employees who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively. Can we infer at the 10% significance level that a difference exists between the two groups?
Test statistic = ______________
Critical Value(s) = ______________
Conclusion: ______________
Interpretation: __________________________________________
Estimate with 90% confidence the difference in mean scores between the two groups of employees.
______________

Accepted Answer

The answer of Thirty-five employees who completed two years of...

Question 9

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as:

Accepted Answer

A)  matched samples 
B)  independent samples 
C)  weighted samples 
D)  random samples 
E)  natural samples

Question 10

The assumption(s) for  to have an F-distribution is (are):

Accepted Answer

A)  random samples are drawn from each of two normal populations 
B)  the samples are independent 
C)  the variability of the measurements in the two populations is the same and can be measured by a common variance, 
D)  all of these are required assumptions 
E)  none of these

Question 11

When testing  vs.  two random samples of sizes 10 and 8, respectively, are used. The calculated value of the test statistic is found to be equal to 2.22. Which of the following statements is true?

Accepted Answer

A)  H0 must be rejected at α = .05 . 
B)  H0 cannot be rejected at α = .05 . 
C)  There is sufficient evidence at α = .05 to conclude that a difference in the population variances exist. 
D)  H0 cannot be rejected at α = .10 . 
E)  None of these.

Question 12

Butch's Dog Kennel boards and trains dogs. There are different breeds and numbers of dogs at the kennel each month. Butch would like to know the variability in the pounds of dog food used each month. A random sample of 12 months yielded the pounds of dog food listed below.
1500, 2300, 2090, 3000, 1980, 1760,
1660, 2470, 3500, 2870, 1300, 1810
Use the data to estimate the population variance using a 99% confidence interval. Assume the distribution is normal.
Use the Data Analysis software if you prefer.
______________ Enter (n1, n2), no commas in numerals

Accepted Answer

The answer of Butch's Dog Kennel boards and trains dogs....

Question 13

The value of F with area 0.05 to its right for  = 6 and  = 9 is 3.37.

Accepted Answer

A) True 
 B)False

Question 14

A psychologist is trying to determine how many hours the average person sleeps each night. He takes a random sample of 25 individuals and asks each person how many hours he or she slept the previous night. The sum of the observations and the sum of the squared observations are:  Estimate with 99% confidence the mean number of hours of sleep.
______________

Accepted Answer

The answer of A psychologist is trying to determine how...

Question 15

A researcher is curious about the effect of sleep on students' test performances. He chooses 50 students and gives each two tests: one given after four hours of sleep and one after eight hours of sleep. The test the researcher should use would be matched pairs t-test.

Accepted Answer

A) True 
 B)False

Question 16

In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference  is normal if:

Accepted Answer

A)  the sample sizes are both greater than 30 
B)  the populations are normal 
C)  the populations are non-normal and the sample sizes are small 
D)  the populations are non-normal and the sample sizes are large 
E)  all of these

Question 17

A two-tailed test for two population variances could have the null hypothesis to be written as  .

Accepted Answer

A) True 
 B)False

Question 18

Do government employees take longer coffee breaks than private sector workers? That is a question that interested a management consultant. To examine the issue, he took a random sample of ten government employees and another random sample of six private sector workers and measured the amount of time (in minutes) they spent in coffee breaks during the day. The results are listed below.  Do these data provide sufficient evidence at the 5% significance level to support the consultant's claim?
Test statistic = ______________
Critical Value(s) = ______________
Conclusion: ______________
Interpretation: ____________________________________________________
Estimate with 95% confidence the difference in coffee breaks mean time between the two groups.
______________

Accepted Answer

The answer of Do government employees take longer coffee breaks...

Question 19

Which of the following statements is false for an F-distribution?

Accepted Answer

A)  Variables that are F distributed range from 0 to. 
B)  Exact shape of the distribution is determined by two numbers of degrees of freedom. 
C)  Degrees of freedom for the denominator are always smaller than the degrees of freedom for the numerator. 
D)  Degrees of freedom for the numerator can be larger, smaller, or equal to the degrees of freedom for the denominator. 
E)  Degrees of freedom for the denominator are always smaller than the degrees of freedom for the numerator and degrees of freedom for the numerator can be larger, smaller, or equal to the degrees of freedom for the denominator.

Question 20

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 10 pairs, is:

Accepted Answer

A)  10 
B)  20 
C)  9 
D)  18 
E)  14

Exam 10: Inference From Small Samples

Regardless of the degrees of freedom, every t-distribution is symmetric around zero.

A random sample of size 25 taken from a normally distributed population resulted in a sample standard deviation of a 0.93054. The lower and upper limits of a 99% confidence interval for the population variance would be:

The chi-squared distribution is:

If a sample of size 20 is randomly selected from a population, the value of A for the probability P(-A t A) = 0.95 is 2.093.

The assumption(s) for to have an F-distribution is (are) :

When testing vs. two random samples of sizes 10 and 8, respectively, are used. The calculated value of the test statistic is found to be equal to 2.22. Which of the following statements is true?

The value of F with area 0.05 to its right for = 6 and = 9 is 3.37.

A researcher is curious about the effect of sleep on students' test performances. He chooses 50 students and gives each two tests: one given after four hours of sleep and one after eight hours of sleep. The test the researcher should use would be matched pairs t-test.

In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference is normal if:

A two-tailed test for two population variances could have the null hypothesis to be written as .

Which of the following statements is false for an F-distribution?

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 10 pairs, is: