Question 1

Use the following information for questions:
 Based on a random sample of 41 flights, the average minutes of airborne time for an airline was 106 minutes, with a standard deviation of 5 minutes.
-Give a 90% confidence interval for the average airborne time for this airline.

Accepted Answer

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 Based...

Question 2

Use the following information for questions:
 Based on a random sample of 41 flights, the average minutes of airborne time for an airline was 106 minutes, with a standard deviation of 5 minutes.
-Would a 95% confidence interval for the average airborne time for this airline be wider or narrower than the 90% confidence interval?

Accepted Answer

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

Question 3

Use the following information for questions:
 Refer to the following statistical summary of the left foot lengths (in centimeters) for a random sample of 76 college men. 
-In terms of the notation of this course, what is the correct way to express the "Mean" shown in the output?

Accepted Answer

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

Question 4

Use the following information for questions:
 Refer to the following statistical summary of the left foot lengths (in centimeters) for a random sample of 76 college men. 
-Complete the following sentence: In about 95% of all samples of this size from this population, the difference between the sample mean and the population mean would be ____.

Accepted Answer

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

Question 5

Use the following information for questions:
 Refer to the following statistical summary of the left foot lengths (in centimeters) for a random sample of 76 college men. 
-Give an approximate 95% confidence interval for the average left foot length for college men.

Accepted Answer

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

Question 6

Use the following information for questions:
 Spatial perception is measured on a scale from 0 to 10. A group of 9S1U1P1thS1S1P0 grade students are tested for spatial perception. SPSS was used to calculate descriptive statistics of the spatial perception scores in the sample. 
-In terms of the notation of this course, what is the correct way to express the value 0.428 in the output?

Accepted Answer

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

Question 7

Use the following information for questions:
 Spatial perception is measured on a scale from 0 to 10. A group of 9S1U1P1thS1S1P0 grade students are tested for spatial perception. SPSS was used to calculate descriptive statistics of the spatial perception scores in the sample. 
-Explain in your own words what the value 0.428 in the output measures.

Accepted Answer

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

Question 8

Use the following information for questions: Spatial perception is measured on a scale from 0 to 10. A group of 9S1U1P1thS1S1P0 grade students are tested for spatial perception. SPSS was used to calculate descriptive statistics of the spatial perception scores in the sample. -Give a 90% confidence interval for the average spatial perception score for all 9^th graders.

Accepted Answer

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

Question 9

Which of the following studies describes a paired data design?
A) The testosterone levels of male doctors and male college professors are compared
B) 40 students measure their blood pressure twice--first while resting and then again after running in place for 10 minutes.
C) The mean blood pressure of men is compared to the mean blood pressure of women
D) All of choices A, B, and C involve paired data.

Accepted Answer

In B, each participant is measured twice under different conditions (resting and after exercise), making the data paired because the measurements are dependent on the same individuals.

Question 10

Which of the following examples involves paired data?
A) A psychologist compares two methods of memorizing information. Twenty people use one method and twenty other people use the second method.
B) A researcher estimates the difference between the mean forearm lengths of men and women based on a random sample of each.
C) A medical researcher measures the cholesterol levels of each of 30 heart attack patients 2 days after the attack and again 4 days after the attack.
D) A marketing research expert estimates the proportion of the 22 to 29 year-old age group that says they might buy a new car in the next two years

Accepted Answer

Paired data involves observations taken on the same subject at two different times or under two different conditions. Option C is an example of paired data because it involves measuring the same group of heart attack patients' cholesterol levels at two different times.

Question 11

Which one of the following ways of collecting data would not result in paired data?
A) Each person is measured twice.
B) Similar individuals are paired prior to an experiment. Each individual in a pair receives a different treatment.
C) Two different variables are measured for each person.
D) Two independent samples are selected and the same response variable is compared between samples.

Accepted Answer

Paired data involves linked observations, such as measurements on the same individual at different times (A), matched individuals receiving different treatments (B), or two variables measured on the same individual (C). Option D describes independent samples, where observations in one sample are not directly linked to observations in the other, thus not resulting in paired data.

Question 12

The multiplier for a confidence interval for one mean or the mean of paired differences depends on
A) The confidence level only.
B) The degrees of freedom only.
C) The confidence level and the degrees of freedom.
D) The confidence level and the sample standard deviation.

Accepted Answer

The multiplier for a confidence interval for one mean or the mean of paired differences depends on both the confidence level and the degrees of freedom. The confidence level affects the critical value from the t-distribution, and the degrees of freedom, which are based on the sample size, affect the shape of the t-distribution.

Question 13

The amount of time the husband and the wife spend on house work is measured for 15 women and their 15 husbands. What are the appropriate degrees of freedom for the multiplier t* for a confidence interval for the difference in mean time spent on housework between husbands and wives?
A) 14
B) 15
C) 29
D) 30

Accepted Answer

The degrees of freedom for a paired t-test, which is used here since the data is paired (husbands and wives), is n-1, where n is the number of pairs. Here, n = 15, so the degrees of freedom is 15 - 1 = 14.

Question 14

The head circumference is measured for 25 girls and their twin sisters. What is the value of the multiplier t* for a 90% confidence interval for the difference in mean head circumference between girl twins?
A) 1.68
B) 2.02
C) 1.71
D) 2.06

Accepted Answer

The correct multiplier t* for a 90% confidence interval when dealing with paired data (such as twins) and a sample size of 25 pairs is found using the t-distribution with n-1 degrees of freedom (here, 24). The value closest to the appropriate t* for a 90% confidence level in the options given is 1.71.

Question 15

Use the following information for questions:
 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. 
-What are the degrees of freedom for this design?
A) 7
B) 8
C) 14
D) 29

Accepted Answer

Degrees of freedom in a statistical test are the number of values in the final calculation of a statistic that are free to vary. In this context, without specific details about the design, the correct answer cannot be determined precisely. However, given only the options, the choice is based on common statistical scenarios or typical setups, which might involve calculations leading to a specific degrees of freedom.

Question 16

Use the following information for questions:
 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. 
-What is the value of the standard error for the difference in mean grades between the two testing methods?
A) 0.395
B) 0.529
C) 0.563
D) 0.660

Accepted Answer

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

Question 17

Use the following information for questions:
 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. 
-Calculate a 98% confidence interval for the difference in mean grades between the two testing methods.
A) (-3.85, -1.44)
B) (-4.03, -1.26)
C) (-4.12, -1.17)
D) (-4.33, -0.95)

Accepted Answer

The correct confidence interval is calculated using the appropriate statistical methods for the given data, resulting in the interval (-4.12, -1.17) for the difference in mean grades between the two testing methods.

Question 18

Use the following information for questions:
 "Sunlight makes everyone feel better." To test this claim, 30 college students receive special lights for their bedrooms that slowly turn on in the morning with imitation sunlight. The experiment takes place in January, when it is still dark out in the morning. Prior to participation, the students fill out a questionnaire to measure their general mood. The average score was 2.73. After three weeks with the special light they fill in the questionnaire again. The average score this time was 3.13. The standard deviation of the differences was 0.822.
-What is the value of the standard error for the difference in average mood score?
A) 0.106
B) 0.150
C) 0.153
D) 0.822

Accepted Answer

The standard error for the difference in average mood score is calculated using the formula for the standard error of the mean difference: SE = s / sqrt(n), where s is the standard deviation of the differences, and n is the sample size. Substituting the given values (s = 0.822, n = 30) into the formula gives SE = 0.822 / sqrt(30) ≈ 0.150.

Question 19

Use the following information for questions:
 "Sunlight makes everyone feel better." To test this claim, 30 college students receive special lights for their bedrooms that slowly turn on in the morning with imitation sunlight. The experiment takes place in January, when it is still dark out in the morning. Prior to participation, the students fill out a questionnaire to measure their general mood. The average score was 2.73. After three weeks with the special light they fill in the questionnaire again. The average score this time was 3.13. The standard deviation of the differences was 0.822.
-Calculate a 95% confidence interval for the difference in average mood scores (after - before).
A) (0.14, 0.66)
B) (0.09, 0.71)
C) (0.19, 0.61)
D) None of the above

Accepted Answer

The answer of Use the following information for questions:
 "Sunlight...

Question 20

Use the following information for questions:
 A manufacturer of cell phones is interested in evaluating two alternative existing layout and flow path designs. Design 1 is the current one in use and Design 2 is a new proposed plan. Both designs were implemented for eight consecutive working days and the output of each design was recorded.
-What are the degrees of freedom for this paired design analysis?
A) 8 (since there are eight days).
B) 16 (since there are 16 observations in all).
C) 15
D) 7

Accepted Answer

The degrees of freedom for a paired design analysis is calculated as n - 1, where n is the number of pairs. Here, n = 8 (eight days of observations for each design), so the degrees of freedom = 8 - 1 = 7.

Quiz 11: Estimating Means With Confidence

Use the following information for questions: Based on a random sample of 41 flights, the average minutes of airborne time for an airline was 106 minutes, with a standard deviation of 5 minutes. -Give a 90% confidence interval for the average airborne time for this airline.

Use the following information for questions: Refer to the following statistical summary of the left foot lengths (in centimeters) for a random sample of 76 college men. -In terms of the notation of this course, what is the correct way to express the "Mean" shown in the output?

Use the following information for questions: Refer to the following statistical summary of the left foot lengths (in centimeters) for a random sample of 76 college men. -Give an approximate 95% confidence interval for the average left foot length for college men.

Which of the following studies describes a paired data design?

Which of the following examples involves paired data?

Which one of the following ways of collecting data would not result in paired data?

The multiplier for a confidence interval for one mean or the mean of paired differences depends on

The amount of time the husband and the wife spend on house work is measured for 15 women and their 15 husbands. What are the appropriate degrees of freedom for the multiplier t* for a confidence interval for the difference in mean time spent on housework between husbands and wives?

The head circumference is measured for 25 girls and their twin sisters. What is the value of the multiplier t* for a 90% confidence interval for the difference in mean head circumference between girl twins?