14 The National Center for Education Statistics would like t

14. The National Center for Education Statistics would like to test the hypothesis that the proportion
of Bachelor\'s degrees that were earned by women equals 0.60. A random sample of 140 college
graduates with Bachelor degrees found that 75 were women. The National Center for Education
Statistics would like to set a = 0.10. The correct hypothesis statement for this hypothesis test would be ?

Solution

Here, n = 140

p = proportion of Bachelor\'s degrees that are earned by women, and we have to test

H0: p = 0.60 (no change)

H1: p != 0.60 (change, two-tailed)

Significance level, a = 0.10

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Using normal distribution,

Mean = np = 140*0.6 = 84

SD = sqrt( n*p* (1-p) ) = sqrt(140*0.6*0.4) = 5.797

Variance = n*p*(1-p) = 140*0.6*0.4 = 33.6

X - N(84, 33.6)

Sample Proportion P (X/n) - N(84/140, 33.6/140^2)

P - N(0.6, 0.0017)

a = 0.10 => Critical Region is z<-1.64 and z>1.64

Now, value of sample proportion = 75/140 = 0.536

So, test static, z = (x - m)/sd = (0.536 - 0.6) / sqrt(0.0017) = -1.55

This value does not lie in the critical region. Thus there is no evidence, at 10% significance level, to support the hypothesis that the propotion of Bachelor\'s degrees that are earned by women equals 0.60