Liberty University BUSI 230 review and exam 4 complete solutions answers and more!

Liberty University BUSI 230 review and exam 4 complete solutions answers and more!

A positive value for a correlation indicates _____.

A researcher reports that there is no consistent relationship between grade point average and the number of hours spent studying for college students. The correlation between grade point average and the number of hours studying is an example of

A negative value for a correlation indicates ______.

Compute the Pearson correlation for the following data.

The value for a correlation can never be greater than 1.00.

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg).

Complete parts (a) through (e), given Σx = 303, Σy = 169, Σx2 = 12163, Σy2 = 3925, Σxy = 5945, and r ≈ -0.923.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

(f) Suppose a car weighs x = 32 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)

Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims.

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong? positive or negative?

(b) Use a calculator to verify that Σx = 128, Σx2 = 6348, Σy = 148, Σy2 = 4710 and Σxy = 2815.

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

For which of the following correlations would the data points be clustered most closely around a straight line?

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 41 women in rural Quebec gave a sample variance s2 = 3.0. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.

(a) What is the level of significance?

State the null and alternate hypotheses.

(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?

What assumptions are you making about the original distribution?

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

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

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

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

Interpret the results in the context of the application.

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.304.

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 s2 ≈ 0.420.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

What assumptions are you making about the original distribution?

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

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

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

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter.

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 24.6, Σx2 = 89.86, Σy = 52.6, Σy2 = 444.72 and Σxy = 191.18.

Compute r. (Round to 3 decimal places.)

Answer

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information.

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 1.957, Σx2 = .553, Σy = 30.3, Σy2 = 152.67 and Σxy = 8.774.

Compute r. (Round to 3 decimal places.)

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).

Complete parts (a) through (e), given Σx = 97, Σy = 623, Σx2 = 2383, Σy2 = 83,181, Σxy = 13,951, and r ≈ 0.999.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r^2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r^2 to three decimal places. Round your answers for the percentages to one decimal place.)

(f) The calves you want to buy are 16 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)

Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.

Complete parts (a) through (e), given Σx = 372, Σy = 115, Σx2 = 24814, Σy2 = 3375, Σxy = 8485, and r ≈ 0.947.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r^2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r^2 to three decimal places. Round your answers for the percentages to one decimal place.)

(f) Predict the percentage of all fatal accidents due to failing to yield the right of way for 70-year-olds. (Round your answer to two decimal places.)

After a large fund drive to help the Boston City Library, the following information was obtained from a random sample of contributors to the library fund. Using a 1% level of significance, test the claim that the amount contributed to the library fund is independent of ethnic group.

(a) What is the level of significance?

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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?

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What sampling distribution will you use?

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What are the degrees of freedom?

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

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

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

The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.

Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site.

(a) What is the level of significance?

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?

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What sampling distribution will you use?

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What are the degrees of freedom?

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

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(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?

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

Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately σ^2 = 136.2. Suppose that for the past 12 years, the variance has been s^2 = 115.5. Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2. Find a 90% confidence interval for the population variance.

(a) What is the level of significance?

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.)

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What are the degrees of freedom?

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What assumptions are you making about the original distribution?

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

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

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

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

Interpret the results in the context of the application.

An economist wonders if corporate productivity in some countries is more volatile than in other countries. One measure of a company's productivity is annual percentage yield based on total company assets.

A random sample of leading companies in France gave the following percentage yields based on assets.

Use a calculator to verify that the sample variance is s^2 ≈ 2.070 for this sample of French companies.

Another random sample of leading companies in Germany gave the following percentage yields based on assets.

Use a calculator to verify that s^2 ≈ 1.176 for this sample of German companies.

Test the claim that there is a difference (either way) in the population variance of percentage yields for leading companies in France and Germany. Use a 5% level of significance. How could your test conclusion relate to the economist's question regarding volatility (data spread) of corporate productivity of large companies in France compared with companies in Germany?

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

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

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What are the degrees of freedom?

What assumptions are you making about the original distribution?

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

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

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

Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.

(i) Give the value of the level of significance.

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State the null and alternate hypotheses.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

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

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(iv) Conclude the test.

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(v) Interpret the conclusion in the context of the application.

A machine that puts corn flakes into boxes is adjusted to put an average of 15.4 ounces into each box, with standard deviation of 0.22 ounce. If a random sample of 18 boxes gave a sample standard deviation of 0.39 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.)

(i) Give the value of the level of significance.

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State the null and alternate hypotheses.

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(ii) Find the sample test statistic. (Round your answer to two decimal places.)

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

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(iv) Conclude the test.

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(v) Interpret the conclusion in the context of the application.

A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 19% were under 20 years old, 11% were in the 20- to 35-year-old bracket, 33% were between 36 and 50, 24% were between 51 and 65, and 13% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

(i) Give the value of the level of significance.

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State the null and alternate hypotheses.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

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

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(iv) Conclude the test.

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(v) Interpret the conclusion in the context of the application.

Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 16 roller bearings from the old manufacturing process showed the sample variance of diameters to be s2 = 0.225. Another random sample of 28 roller bearings from the new manufacturing process showed the sample variance of their diameters to be s2 = 0.115. Use a 5% level of significance to test the claim that there is a difference (either way) in the population variances between the old and new manufacturing processes.

Classify the problem as being a Chi-square test of independence or homogeneity, Chi-square goodness-of-fit, Chi-square for testing or estimating σ2 or σ, F test for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.

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(i) Give the value of the level of significance.

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State the null and alternate hypotheses.

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(ii) Find the sample test statistic. (Round your answer to two decimal places.)

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(iii) Find the P-value of the sample test statistic.

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(iv) Conclude the test.

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(v) Interpret the conclusion in the context of the application.

Suppose the scatter diagram of a random sample of data pairs (x, y) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, –1, or 0?