Liberty University BUSI 230 week 8 exercises 10.1-10.4 complete solutions answers and more!

Liberty University BUSI 230 week 8 exercises 10.1-10.4 complete solutions answers and more!

Question 1

In general, are chi-square distributions symmetric or skewed? If skewed, are they skewed right or left?

Question 2

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.

occupation

Clegry

M.D.

Lawyer

Column Total

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Answer

(e) Interpret your conclusion in the context of the application.

Question 3

The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Age

Calf

Yearling

Adult

Column Total

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Answer

(e) Interpret your conclusion in the context of the application.

Question 4

The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.

Myers-Briggs Preference

IN

EN

IS

ES

Column Total

Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Answer

(e) Interpret your conclusion in the context of the application.

Question 5

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What sampling distribution will you use?

Answer

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Answer

(e) Interpret your conclusion in the context of the application.

Question 6

For a chi-square goodness-of-fit test, how are the degrees of freedom computed?

Question 7

The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below.

Type of Household

Married with children

Married, no children

Single parent

One person

Other

Total

Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

Answer

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Answer

(e) Interpret your conclusion in the context of the application.

Question 8

The types of browse favored by deer are shown in the following table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer.

Type of Browse

Sage brush

Rabbit brush

Salt brush

Service berry

other

Total

Use a 5% level of significance to test the claim that the natural distribution of browse fits the deer feeding pattern.

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

Answer

(c) Estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Answer

(e) Interpret your conclusion in the context of the application.

Question 9

The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below.

Subject Area

Business

Humanities

Natural Science

Social Science

All other subjects

Total

Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students.

State the null and alternate hypotheses.

Answer

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

Answer

(c) Estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Answer

(e) Interpret your conclusion in the context of the application.

Question 10

The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown below.

Ethnic Origin

Black

Asian

Anglo

Latino/Latina

Native American

All others

Total

Using a 1% level of significance, test the claim that the census distribution and the sample distribution agree.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

Answer

(c) Estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Answer

(e) Interpret your conclusion in the context of the application.

Question 11

A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance σ2 = 42.3. In a different section of Chaco Canyon, a random sample of 20 transects gave a sample variance s2 = 44.5 for the number of sites per transect. Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3. Find a 95% confidence interval for the population variance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

Answer

What are the degrees of freedom?

Answer

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

Answer

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

lower limit

upper limit

Interpret the results in the context of the application.

Question 12

Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2 = 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance s2 = 82.6. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Find a 95% confidence interval for the population variance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

Answer

What are the degrees of freedom?

Answer

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

Answer

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

lower limit

upper limit

Interpret the results in the context of the application.

Question 13

A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 29 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.3 months. Using a 0.05 level of significance, test the claim that the new typhoid shot has a smaller variance of protection times.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

Answer

What are the degrees of freedom?

Answer

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

Answer

(f) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

lower limit

upper limit

Interpret the results in the context of the application.

Question 14

Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and other times he becomes worried about prize bulls that take too long to recover. By reading journals, Jim has found that the tranquilizer should have a mean duration time of 65 minutes, with a standard deviation of 15 minutes. A random sample of 8 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 26 minutes. At the 1% level of significance, is Jim justified in the claim that the variance is larger than that stated in his journal? Find a 95% confidence interval for the population standard deviation.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

Answer

What are the degrees of freedom?

Answer

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

Answer

(f) Find the requested confidence interval for the population standard deviation. (Round your answers to two decimal place.)

lower limit

upper limit

Interpret the results in the context of the application.

Question 15

To use the F distribution, what degrees of freedom need to be calculated?

Question 16

Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).

Use a calculator to verify that, for this plot, the sample variance is s^2 ≈ 0.306.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s^2 ≈ 0.091.

Test the claim that the population variance of annual wheat production for the first plot is larger than that for the second plot. Use a 1% level of significance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

dfN 

dfD 

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

Question 17

You don't need to be rich to buy a few shares in a mutual fund. The question is, how reliable are mutual funds as investments? This depends on the type of fund you buy. The following data are based on information taken from a mutual fund guide available in most libraries.

A random sample of percentage annual returns for mutual funds holding stocks in aggressive-growth small companies is shown below.

Use a calculator to verify that s^2 ≈ 349.277 for the sample of aggressive-growth small company funds.

Another random sample of percentage annual returns for mutual funds holding value (i.e., market underpriced) stocks in large companies is shown below.

16.5

-0.5

Use a calculator to verify that s^2 ≈ 136.538 for value stocks in large companies.

Test the claim that the population variance for mutual funds holding aggressive-growth in small companies is larger than the population variance for mutual funds holding value stocks in large companies. Use a 5% level of significance. How could your test conclusion relate to the question of reliability of returns for each type of mutual fund?

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

Answer

What are the degrees of freedom?

dfN 

dfD 

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

dfN 

dfD 

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

Question 18

A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26 temperature readings gave a sample variance of 4.6. Another similar frozen food case was equipped with the old thermostat, and a random sample of 15 temperature readings gave a sample variance of 12.3. Test the claim that the population variance of the new thermostat temperature readings is smaller than that for the new thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.)

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)

Answer

What are the degrees of freedom?

dfN 

dfD 

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.

Question 19

A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 41 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was 55.1. Another random sample of 22 trucks were fitted with the old fuel injection system and driven under a variety of different conditions. For these trucks, the sample variance of gasoline consumption was 34.6. Test the claim that there is a difference in population variance of gasoline consumption for the two injection systems. Use a 5% level of significance. How could your test conclusion relate to the question regarding the consistency of fuel consumption for the two fuel injection systems?

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

Answer

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)

Answer

What are the degrees of freedom?

dfN 

dfD 

What assumptions are you making about the original distribution?

Answer

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer

(e) Interpret your conclusion in the context of the application.