Statistics. 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.
| Personality Type | |||
| Occupation | E | I | Row Total |
| Clergy (all denominations) | 62 | 45 | 107 |
| M.D. | 65 | 97 | 162 |
| Lawyer | 61 | 76 | 137 |
| Column Total | 188 | 218 | 406 |
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?
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Order Paper Now- 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.)
- c) What are the degrees of freedom?
The following table shows age distribution and location of a random sample of 166 buffalo in a national park.
| Age | Lamar District | Nez Perce District | Firehole District | Row Total |
| Calf | 16 | 15 | 10 | 41 |
| Yearling | 13 | 12 | 8 | 33 |
| Adult | 38 | 29 | 25 | 92 |
| Column Total | 67 | 56 | 43 | 166 |
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?
(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 are the degrees of freedom?
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 |
Arts & Science | Business | Allied Health | Row Total |
| IN | 68 | 10 | 18 | 96 |
| EN | 86 | 39 | 29 | 154 |
| IS | 52 | 39 | 24 | 115 |
| ES | 80 | 41 | 33 | 154 |
| Column Total | 286 | 129 | 104 | 519 |
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?
(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 are the degrees of freedom?
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.
| Person’s Age | ||||
| Movie | 18-23 yr | 24-29 yr | 30-35 yr | Row Total |
| Drama | 6 | 13 | 15 | 34 |
| Science Fiction | 15 | 9 | 6 | 30 |
| Comedy | 9 | 9 | 11 | 29 |
| Column Total | 30 | 31 | 32 | 93 |
(a) What is the level of significance?
(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 are the degrees of freedom?
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 | Percent of U.S. Households |
Observed Number of Households in the Community |
| Married with children | 26% | 93 |
| Married, no children | 29% | 115 |
| Single parent | 9% | 33 |
| One person | 25% | 98 |
| Other (e.g., roommates, siblings) | 11% | 72 |
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?
(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.)
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.)
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 | Plant Composition in Study Area |
Observed Number of Deer Feeding on This Plant |
| Sage brush | 32% | 95 |
| Rabbit brush | 38.7% | 135 |
| Salt brush | 12% | 41 |
| Service berry | 9.3% | 30 |
| Other | 8% | 19 |
Use a 5% level of significance to test the claim that the natural distribution of browse fits the deer feeding pattern.
(a) What is the level of significance?
(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 are the degrees of freedom?
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 | Percent of Books on Subject in Circulation Library on This Subject |
Number of Books in Sample on This Subject |
| Business | 32% | 286 |
| Humanities | 25% | 209 |
| Natural Science | 20% | 220 |
| Social Science | 15% | 107 |
| All other subjects | 8% | 66 |
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.
(a) What is the level of significance?
(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to three decimal places. Round the test statistic to three decimal places.)
What are the degrees of freedom?
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 | Census Percent | Sample Result |
| Black | 10% | 137 |
| Asian | 3% | 37 |
| Anglo | 38% | 464 |
| Latino/Latina | 41% | 512 |
| Native American | 6% | 52 |
| All others | 2% | 13 |
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?
(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 are the degrees of freedom?
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 26 transects gave a sample variance s2 = 46.3 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?
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)
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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 16 colleges and universities in Kansas showed that x has a sample variance s2 = 80.5. 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?
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)
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| upper limit |
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 25 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.5 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?
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
(f) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)
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| upper limit |
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 14 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?
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
(f) Find the requested confidence interval for the population standard deviation. (Round your answers to two decimal place.)
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| upper limit | min |
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).
| 3.66 | 3.75 | 4.29 | 3.90 | 3.81 | 3.79 | 4.09 | 4.42 |
| 3.89 | 3.87 | 4.12 | 3.09 | 4.86 | 2.90 | 5.01 | 3.39 |
Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.311.
Another random sample of years for a second plot gave the following annual wheat production (in pounds).
| 3.97 | 3.67 | 3.49 | 3.91 | 3.40 | 3.72 | 4.13 | 4.01 |
| 3.59 | 4.29 | 3.78 | 3.19 | 3.84 | 3.91 | 3.66 | 4.35 |
Use a calculator to verify that the sample variance for this plot is s2 ≈ 0.098.
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?
(b) Find the value of the sample F statistic. (Use 2 decimal places.)
What are the degrees of freedom?
| dfN | |
| dfD |
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.
| -1.9 | 14.6 | 41.2 | 17.2 | -16.7 | 4.4 | 32.6 | -7.3 | 16.2 | 2.8 | 34.3 |
| -10.6 | 8.4 | -7.0 | -2.3 | -18.5 | 25.0 | -9.8 | -7.8 | -24.6 | 22.8 |
Use a calculator to verify that s2 ≈ 347.471 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.
| 16.3 | 0.5 | 7.7 | -1.9 | -3.6 | 19.4 | -2.5 | 15.9 | 32.6 | 22.1 | 3.4 |
| -0.5 | -8.3 | 25.8 | -4.1 | 14.6 | 6.5 | 18.0 | 21.0 | 0.2 | -1.6 |
Use a calculator to verify that s2 ≈ 137.294 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?
(b) Find the value of the sample F statistic. (Use 2 decimal places.)
What are the degrees of freedom?
| dfN | |
| dfD |
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 21 temperature readings gave a sample variance of 4.7. Another similar frozen food case was equipped with the old thermostat, and a random sample of 16 temperature readings gave a sample variance of 12.5. Test the claim that the population variance of the old thermostat temperature readings is larger 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?
(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)
What are the degrees of freedom?
| dfN | = |
| dfD | = |
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 31 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was 55.7. Another random sample of 27 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 37. 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?
(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)
What are the degrees of freedom?
| dfN | |
| dfD |
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