A medical researcher claims that a specially treated...

A medical researcher claims that a specially treated intravenous solution decreases the variance of the time required for nutrients to enter the bloodstream. Independent samples from each type of solution are randomly selected, and the results are shown in the table at the left. At ? = 0.01, is there enough evidence to support the researcher's claim? Assume the populations are normally distributed. Normal solution Treated solution n = 25 n = 20 s^2 = 180 s^2 = 56 a. Identify the claim and state H0 and Ha. b. Specify the level of significance ?. c. Determine the degrees of freedom for the numerator and for the denominator. d. Determine the critical value and the rejection region. e. Use the F-test to find the test statistic F. Sketch a graph. f. Decide whether to reject the null hypothesis. g. Interpret the decision in the context of the original claim.

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Medical researchers claim that specially treated intravenous solution reduces the time required for nutrients to enter the bloodstream. Independent samples from each type of solution are randomly selected, and the results are shown in the table on the left. At Î± = 0.01, is there enough evidence to support the researcher's claim? Assume the populations are normally distributed. Solution Type: Normal Treated Solution Sample Size: n = 25 Sample Mean: 180 Solution Type: Solution Sample Size: n = 20 Sample Mean: 56 Identify the claim and state Ho and Ha: Claim: Specially treated intravenous solution decreases the time required for nutrients to enter the bloodstream. Ho: The mean time required for nutrients to enter the bloodstream is the same for both types of solutions. Ha: The mean time required for nutrients to enter the bloodstream is different for the two types of solutions. b. Specify the level of significance: Î± = 0.01 d. Determine the degrees of freedom for the numerator and for the denominator: Degrees of freedom for the numerator (df1): n1 - 1 = 25 - 1 = 24 Degrees of freedom for the denominator (df2): n2 - 1 = 20 - 1 = 19 Determine the critical value and the rejection region: Using the F-test, we need to find the critical value from the F-distribution table with df1 = 24 and df2 = 19 at Î± = 0.01. The critical value is F0.01(24, 19) = 2.85. Rejection Region: Reject Ho if the test statistic F is greater than 2.85 or less than 1/2.85. Use the F-test to find the test statistic F: F = (Sample Variance of Normal Treated Solution) / (Sample Variance of Solution) F = (180) / (56) Sketch a graph: [Graph] Decide whether to reject the null hypothesis: If the calculated test statistic F is greater than 2.85 or less than 1/2.85, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis. Interpret the decision in the context of the original claim: Based on the results of the F-test, we will determine whether there is enough evidence to support the claim that specially treated intravenous solution decreases the time required for nutrients to enter the bloodstream.

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