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# Statistics 2

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?

At the 0.05 level of significance, what is the critical value?

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.

If you are interested in determining if there is sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies, what is/are the critical value you would use to conduct such a test of hypothesis?

Place your answer, rounded to 2 decimal places, in the blank. If there are two critical values, place only the positive value in the blank. For example, 2.34 would be a legitimate entry.

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:

percent change for corporation 15 12 3 12 28 6 8 2
percent change for CEO 6 17 -4 12 32 -1 7 2

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.

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.

Version A Version B
Sample size 45 65
Mean score 8.8 8.2
Sample variance 2.6 2.4

What is the test value for this hypothesis test?

What is/are the critical value(s) for this hypothesis test? If there are two critical values, give only the positive value.

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.

A negative relationship between an explanatory variable X and a response variable Y means that as X increases, Y decreases, and vice versa.

Is it true or false?

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.

Is it True or False?

#### Solution Preview

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?
The test statistic used is , where S1 = 43, S2 = 23, n1 = 8, n2 = 12
Therefore, = 1.87

At the 0.05 level of significance, what is the critical value?
Critical value = 3.76
Hint:
Critical value is obtained from the F-distribution table with d.f. (7, 11) at the significance level 0.05.

Details
F Test for Differences in Two Variances

Data
Level of Significance 0.05
Larger-Variance Sample
Sample Size 8
Sample Variance 43
Smaller-Variance Sample
Sample Size 12
Sample Variance 23

Intermediate Calculations
F Test Statistic 1.869565217
Population 1 Sample Degrees of Freedom 7
Population 2 Sample Degrees of Freedom 11

Two-Tail Test
Upper Critical Value 3.758637919
p-Value 0.339781839
Do not reject the null hypothesis

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.
If you are interested in determining if there is ...

#### Solution Summary

The expert examines test values for hypothesis tests. The levels of significance for a critical value are provided.

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