Question 1

When comparing two means, which situation is most likely to lead to a result that is statistically significant? (Consider all other factors equal, such as significance level and standard deviations.)

Accepted Answer

A)    x‾1\overline{x}_1x1​  = 10,  x‾2\overline{x}_2x2​  = 20 and the sample sizes are  n1n_1n1​  = 25 and  n2n_2n2​  = 25
B)    x‾1\overline{x}_1x1​  = 10,  x‾2\overline{x}_2x2​  = 25 and the sample sizes are  n1n_1n1​  = 25 and  n2n_2n2​  = 25
C)    x‾1\overline{x}_1x1​  = 10,  x‾2\overline{x}_2x2​  = 20 and the sample sizes are  n1n_1n1​  = 15 and  n2n_2n2​  = 20
D)    x‾1\overline{x}_1x1​  = 10,  x‾2\overline{x}_2x2​  = 25 and the sample sizes are  n1n_1n1​  = 25 and  n2n_2n2​  = 35  D

Question 2

What is the estimated effect size for a test for the difference between two population means with independent samples with sizes of 25 and 35 respectively and a pooled t-test statistic of t = -2.34?

Accepted Answer

A)   0.23
B)   -0.43
C)   -0.61
D)   -0.16 C

Question 3

Use the following information for questions:
 It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resultingt-statistic was 1.80.
-This is an example of

Accepted Answer

A)   a two-sample t-test.
B)   a paired t-test.
C)   a pooled t-test.
D)   an unpooled t-test. B

Question 4

Use the following information for questions:
 A pooled two independent samples t-test was conducted to compare the average number of accidents for male drivers to that for female drivers. The t-test statistic was 2.4 and the sample sizes were 32 males and 30 females.
-Based on Cohen's interpretation, this effect is

Accepted Answer

A)   a small effect, not obvious without statistics.
B)   a medium effect, obvious to careful observers.
C)   a large effect, obvious to most observers.

Question 5

Use the following information for questions:
 It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resultingt-statistic was 1.80.
-Which of the following is an appropriate conclusion?

Accepted Answer

A)   The results are statistically significant so the left hand appears to be stronger.
B)   The results are statistically significant so the left hand does not appear to be stronger.
C)   The results are not statistically significant so there is not enough evidence to conclude the left hand appears to be stronger.
D)   None of the above.

Question 6

A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion?

Accepted Answer

A)   Conclude that the population average is 70.
B)   Conclude that the population average is 71.8.
C)   Reject the hypothesis that the population average is 70.
D)   Reject the hypothesis that the sample average is 70.

Question 7

Use the following information for questions:
 A sample of n = 9 men are asked. "What's the fastest you've ever driven a car?"The sample mean is 120 mph and the standard deviation is 30.
-Find the p-value for testing whether the population mean response is more than 100 mph?

Accepted Answer

The answer of Use the following information for questions:
 A...

Question 8

Use the following information for questions:
 A small bakery is trying to predict how many loaves of bread to bake daily. They randomly sample daily sales records from the past year. In these days, the bakery sold between 40 and 80 loaves per day with a 95% confidence interval for the population mean daily loaf demand given by (51, 54).
-How would a 99% confidence interval compare to the 95% confidence interval?

Accepted Answer

A)   It would be wider.
B)   It would be narrower.
C)   It would be the same width.
D)   Cannot be determined.

Question 9

Use the following information for questions:
 A small bakery is trying to predict how many loaves of bread to bake daily. They randomly sample daily sales records from the past year. In these days, the bakery sold between 40 and 80 loaves per day with a 95% confidence interval for the population mean daily loaf demand given by (51, 54).
-Based on this interval, what is the decision for testing H0: $\mu$ = 50 versus Ha: $\mu$$\neq$50 at the 10% significance level?

Accepted Answer

A)   Reject the null hypothesis.
B)   Fail to reject the null hypothesis.
C)   Cannot be determined.

Question 10

An experiment is conducted with 15 seniors who are taking Spanish at Oak View High School. A randomly selected group of eight students is first tested with a written test and a day later with an oral exam. To avoid order effects, the other seven students are tested in reverse order. The instructor is interested in the difference in grades between the two testing methods. SPSS is used to obtain descriptive statistics for the grades of the two tests. 
 Is there a significant difference between the mean grades using the two different testing methods? Use $\alpha$ = 0.05.

Accepted Answer

A)   Yes, because t = -4.69 and the p-value 
B)   No, because t = -1.21 and the p-value > 0.05.
C)   Yes, because t = -6.63 and the p-value 
D)   No, because t =-1.48 and the p-value > 0.05.

Question 11

Use the following information for questions:
 A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let $µ_1$ = average age of onset for women and $µ_2$= average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, do not assume the population variances are equal, and use the conservative "by hand" estimate for the degrees of freedom.
-What is the p-value?

Accepted Answer

A)   p-value = 0.009
B)   p-value = 0.018
C)   p-value = 0.015
D)   None of the above

Question 12

Use the following information for questions:
 A small bakery is trying to predict how many loaves of bread to bake daily. They randomly sample daily sales records from the past year. In these days, the bakery sold between 40 and 80 loaves per day with a 95% confidence interval for the population mean daily loaf demand given by (51, 54).
-Based on this interval, what is the decision for testing H0: $\mu$ = 50 versus Ha: $\mu$$\neq$50 at the 5% significance level?

Accepted Answer

A)   Reject the null hypothesis.
B)   Fail to reject the null hypothesis.
C)   Cannot be determined.

Question 13

The average time in years to get an undergraduate degree in computer science was compared for men and women. Random samples of 100 male computer science majors and 100 female computer science majors were taken. Choose the appropriate parameter(s) for this situation.

Accepted Answer

A)   P
B)    p1p_1p1​ - p2p_2p2​ 
C)    µµµ 
D)    µ1µ_1µ1​ - µ2µ_2µ2​

Question 14

Spatial perception is measured on a scale from 0 to 10. A group of 9th grade students are tested for spatial perception. SPSS was used to obtain descriptive statistics of the spatial perception scores in the sample.  
Using $\alpha$ = 0.01, is the mean score significantly different from 5?

Accepted Answer

A)   Yes, because t = 2.34 and this is greater than t* = 2.11.
B)   No, because t = 2.34 and this is smaller than t* = 3.97.
C)   No, because t = 0.55 and this is smaller than t* = 2.11.
D)   No, because t = 2.34 and this is smaller than t* = 2.90.

Question 15

Use the following information for questions:
 A safety officer wants to prove that $\mu$ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed.
-What are the appropriate null and alternative hypotheses?

Accepted Answer

A)   H0:  μ\muμ = 25 and Ha:  μ\muμ  
B)   H0:  μ\muμ  = 25 and Ha:  μ\muμ  >25.
C)   H0:  μ\muμ  = 25 and Ha:  μ\muμ   ≠
eq=  25.
D)   H0:  μ\muμ   ≠
eq= 25 and Ha:  μ\muμ  = 25.

Question 16

Use the following information for questions:
 A group of women suffering from various types of obsessive fear is given a therapeutic course to learn how to handle their fear. At the beginning of the course the women are given a questionnaire to determine how afraid they are. Fear scores range between 100 and 400. SPSS is used to obtain descriptive statistics. Output is shown below.  The course coordinator wishes to test if the women score significantly lower than 250.
-What is the value of the t-test statistic?

Accepted Answer

The answer of Use the following information for questions:
 A...

Question 17

Use the following information for questions:
 A bank official wants to assess if the average delays for two airlines are different.Let $µ_1$ = average delay for Airline 1 and $µ_2$ = average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 6 minutes delay with a standard deviation of 5 minutes. A random sample of 10 flights for Airline 2 shows an average of 12 minutes delay with a standard deviation of 5 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom.
-Are the results statistically significant?

Accepted Answer

A)   No, results are not statistically significant because | t | 
B)   Yes, results are statistically significant because | t | > 2.26.
C)   No, results are not statistically significant because | t | > 2.26.
D)   None of the above.

Question 18

The primary purpose of a significance test is to

Accepted Answer

A)   estimate the p-value of a sample.
B)   estimate the p-value of a population.
C)   decide whether there is enough evidence to support a research hypothesis about a sample.
D)   decide whether there is enough evidence to support a research hypothesis about a population.

Question 19

Use the following information for questions:
A large car insurance company is conducting a study to see if male and female drivers have the same number of accidents, on average, or if male drivers (who tend to be thought of as more aggressive drivers) have more. Data on the number of accidents in the past 5 years is collected for randomly selected drivers who are insured by this company. An analysis of the results produced the following output.  
-Note that the p-value for the two-sided test is p = 0.0193. What would be the p-value for the one-sided test of interest here?

Accepted Answer

The answer of Use the following information for questions:
A large...

Question 20

Use the following information for questions:
 An airport official wants to assess if the flights from one airline (Airline 1) are less delayed than flights from another airline (Airline 2). Let $µ_1$ = average delay for Airline 1 and $µ_2$ = average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 9.5 minutes delay with a standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a standard deviation of 3 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom.
-What are the appropriate null and alternative hypotheses?

Accepted Answer

A)   H0:  µ1µ_1µ1​  -  µ2µ_2µ2​  = 0 and Ha:  µ1µ_1µ1​ - µ2µ_2µ2​   ≠
eq=  0
B)   H0:  µ1µ_1µ1​ - µ2µ_2µ2​   ≠
eq=  0 and Ha:  µ1µ_1µ1​ - µ2µ_2µ2​  = 0
C)   H0: µ1µ_1µ1​ - µ2µ_2µ2​  = 0 and Ha: µ1µ_1µ1​ - µ2µ_2µ2​  
D)   H0:  µ1µ_1µ1​ - µ2µ_2µ2​  = 0 and Ha:  µ1µ_1µ1​ - µ2µ_2µ2​  > 0

Exam 13: Testing Hypotheses About Means

When comparing two means, which situation is most likely to lead to a result that is statistically significant? (Consider all other factors equal, such as significance level and standard deviations.)

What is the estimated effect size for a test for the difference between two population means with independent samples with sizes of 25 and 35 respectively and a pooled t-test statistic of t = -2.34?

A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion?

Use the following information for questions: A sample of n = 9 men are asked. "What's the fastest you've ever driven a car?"The sample mean is 120 mph and the standard deviation is 30. -Find the p-value for testing whether the population mean response is more than 100 mph?

The average time in years to get an undergraduate degree in computer science was compared for men and women. Random samples of 100 male computer science majors and 100 female computer science majors were taken. Choose the appropriate parameter(s) for this situation.

Spatial perception is measured on a scale from 0 to 10. A group of 9th grade students are tested for spatial perception. SPSS was used to obtain descriptive statistics of the spatial perception scores in the sample. Using α\alphaα = 0.01, is the mean score significantly different from 5?

The primary purpose of a significance test is to