42. Find the P-value for each F test value. a. F-2.97,d.f.N. 9, d.f.D. 14, right

Question

42. Find the P-value for each F test value. a. F-2.97,d.f.N. 9, d.f.D. 14, right-tailed b. F 3.32, d.f.N. 6, d.f.D. 12, two-tailed 2.28, d.f.N. 12, d.f.D. 20, right-tailecd F = 3.51, df.?. = 12, d.f.D. = 21, right-tailed C. F d. 43. In a hospital study, it was found that the standard deviation of the sound levels from 20 randomly selected areas designated as "casualty doors" was 44 dB and the standard deviation of 24 randomly selected areas designated as operating theaters was 7.5 dB. At a -0.05, can you substantiate the claim that there is a difference in the standard deviations? 44. A random sample of daily high temperatures in January and February is listed. At a- 0.05 can it be concluded that there is a difference in variances in high temperature between the two months? 9 Jan. 31 31 38 24 24 42 43 35 42 Feb.31 29 24 30 28 24 27 34 27 45. A medical researcher wishes to see whether the variance of the heart rates in beats per minute) of smokers is different from the variance of heart rates of people who do not smoke. Two samples are selected, and the data are shown. Using alpha equal to 0.05, is there enough evidence to support the claim? Assume the variable is normally distributed 2 Nonsmokers Smokers n1 26 s12 36 S22 10

Explanation / Answer

#43.

Null and alternate hypothesis are

H0: ?1 = ?2

Ha: ?1 ? ?2 (two-tailed test)

Test Statistic: F = s1^2/s2^2 = 4.1^2/7.5^2 = 0.2988

Fcritical (19,23) at 0.05 significance level

F(0.975, 19, 23) = 2.3745

F(0.025, 19, 23) = 0.4057

As test statistics is less than F(0.025, 19, 23), we reject the null hypothesis.

This means there std. dev. or variances are not equal.

#44.

Null and alternate hypothesis are

H0: ?1^2 = ?2^2

Ha: ?1^2 ? ?2^2 (two-tailed test)

Test Statistic: F = s1^2/s2^2 = 64.622/10.44 = 6.1872

Fcritical (9,8) at 0.05 significance level

F(0.975, 9, 8) = 4.3572

F(0.025, 9, 8) = 0.2438

As test statistics is greater than F(0.975, 9, 8), we reject the null hypothesis.

This means there std. dev. or variances are not equal.

Jan Feb n 10 9 Var 64.62222 10.44444

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