STATS 17 questions

Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies. Is there sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies?

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Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if the amount of money spent by its female charge customers differs, on average, from the amount spent by its male charge customers. To answer this question, an analyst collected random samples of 25 female customers and 22 male customers. Based on these samples, on average, the 25 women charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover, the sample standard deviation of the amount charged by the 25 women was $93.393, and the sample standard deviation of the amount charged by the 22 men was $59.695. Using the procedure advocated by Bluman,  at the 10% level of significance, is there sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women charge customers differs from the amount spent by men charge customers.

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A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men.  Assume α = 0.05.  What is the test value?

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The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. .

Is the correlation between weekly sales and shelf space significant at the .01 level of significance?

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The correlation value ranges from

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In a simple linear regression analysis, the following sum of squares are produced: = 500 = 100 = 400 The proportion of the variation in Y that is explained by the variation in X is:

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In regression analysis, the variable we are trying to explain or predict is called the

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A correlation value of zero indicates.

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Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A business major wants to determine whether the variation in advertising costs of hair salons is different from the variation in advertising costs of nail salons.  He surveys several businesses and finds the standard deviation in monthly advertising costs is $23 for 12 hair salons, and $43 for 8 nail salons. What is the test value for this hypothesis test? Test value: Round your answer to two decimal places. At the 0.05 level of significance, what is the critical value? Critical value:   Round your answer to two decimal places.

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsx Treating ILE as the response variable, use regression to fit a straight line to all 18 data points.  Based on your results, If direct labor hours (DLH) increases by one hour, the indirect labor expense (ILE), on average, increases by approximately how much? Place your answer, rounded to 2 decimal places, in the blank.  Do not use any stray punctuation marks or a dollar sign.  For example, 34.56 would be a legitimate entry.

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsx Treating ILE as the response variable, use regression to fit a straight line to all 18 data points.  Approximately what percentage of the variation in indirect labor expenses is explained by the regression model you derived? Place your answer, rounded to 1 decimal place, in the blank.  Do not use any stray punctuation marks or a percentage sign.  For example, 78.9 would be a legitimate entry.

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Are America’s top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO’s annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the test value that you would use to conduct this test of hypothesis?  Place your answer, rounded to 3 decimal places, in the blank.  For example, 2.345 would be a legitimate entry.

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if the amount of money spent by its female charge customers differs, on average, from the amount spent by its male charge customers. To answer this question, an analyst collected random samples of 25 female customers and 22 male customers.  Based on these samples, on average, the 25 women charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover, the sample standard deviation of the amount charged by the 25 women was $93.393, and the sample standard deviation of the amount charged by the 22 men was $59.695. Suppose, using a 10% level of significance, you wish to know if there is sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women charge customers differs from the amount spent by men charge customers. That is suppose you wish to test H0:   versus  H1:  Assuming that the amounts spent by male and female charge customers at Q-Mart are normally distributed, based on the procedure advocated by Bluman, what is the test value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry.

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A professor gives an exam for which there are two versions, A and B.  Each student in the class is given one randomly selected version of the exam.   After the exam, the professor wishes to determine if there is a difference in the level of difficulty of the two versions by determining if there is a significant difference in the mean scores.  Assume α = 0.05.

What is the test value for this hypothesis test? Answer:    Round your answer to two decimal places. What is/are the critical value(s) for this hypothesis test?  If there are two critical values, give only the positive value. Answer:    Round your answer to two decimal places. What is the conclusion for this hypothesis test?  Choose one. 1.  There is not sufficient evidence to show that one version of the exam is more difficult than the other. 2.  There is sufficient evidence to show that one version of the exam is more difficult than the other. Answer:    Enter only a 1 or 2 for your answer.

The number of degrees of freedom associated with the t-test, when the data are gathered from a paired samples experiment with 12 pairs, is 24.

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In a simple linear regression problem, the least squares line is y’ = -3.2 + 1.3X, and the coefficient of determination is 0.7225. The coefficient of correlation must be –0.85.

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If there is no linear relationship between two variables X and Y, the coefficient of determination, R2, must be 1.0.

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