We would like to compare the characteristics of tuberculosis meningitis in patients infected with HIV and those who are not infected. In particular we would like to determine whether the two populations have the same mean age. A sample of \" 37 infected patients has mean age 27.9 years and a standard deviation 5.6 years. A sample of 19 patients who are not infected has mean age 36.8 years and standard deviation 21.7 years. Conduct a hypothesis lest to check for equality of variances State the null and alternate hypotheses Ho versus Ha Compute the F test statistic State the numerator and denominator deg of freedom , State the critical value obtained from the F table State your conclusion regarding the variances Based on (a), what tesl will you use to determine If the 2 populations have the same mean age?
n Sample size 37 19
x bar Mean 27.9 38.8
sigma sd 5.6 21.7
Alpha = 0.05
F = s2^2/s1^2 = 15.295
H0: var I = var II
Ha: var 1 not equals var II
Since second variance is more this is a right tailed test.
p value for df, 36,18 is
= 0.000006
As p value < 0.05
reject null hypothesis.
The variances have significant differences.
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