An investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock is to measure the variation in the stock’s daily price changes. 

In an effort to test the claim that the variance in the daily stock price changes for stock 1 is different from the variance in the daily stock price changes for stock 2, the investor obtains a random sample of 21 daily price changes for stock 1 and 21 daily price changes for stock 2. 

The summary statistics associated with these samples are: n
₁ = 21, s
₁ = .725, n
₂ = 21, s
₂ = .529. 

If you compute the test value by placing the larger variance in the numerator, at the .05 level of significance, would you conclude that the risks associated with these two stocks are different? 

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Serum ferritin is used in diagnosing iron deficiency. In a study conducted recently researchers discovered that in a sample of 28 elderly men the sample standard deviation of serum ferritin was 52.6 mg/L. For 26 younger men the sample standard deviation was 84.2 mg/L. At the .01 level of significance, do these data support the conclusion that the ferritin distribution in elderly men has a smaller variance than in younger men?

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Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. 

At the .01 level of significance, is there sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?

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The standard error of the estimate, s
_est, is essentially the

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The correlation value ranges from

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Outliers are observations that

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A correlation value of zero indicates.

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Correlation is a summary measure that 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: