2 Random samples of 50 women and 50 men are taken at Ohio Un

2. Random samples of 50 women and 50 men are taken at Ohio University. They are asked their reaction to increased tuition fees. Of the women, 22 favored the increase. Of the men, 18 favor the increase. At a 10% significance level, does this indicate that a larger proportion of women favor the increase than men? If a test of significance is warranted clearly indicate the following steps:

Step 1: (State the null and alternative hypothesis.)

Step 2: (Calculate the test statistic) T/Z =

Step 3: (Find the p-value) =

Step 4: (State the Conclusion in sentence form) Reject/Accept the null hypothesis because

Solution

Step 1: (State the null and alternative hypothesis.)

Let p1 be the proportion for women

Let p2 be the proportion for men

Null hypothesis: p1=p2

Alternative hypothesis: p1>p2

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Step 2: (Calculate the test statistic)

p1=22/50 =0.44

p2=18/50 =0.36

Z = (p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.44-0.36)/sqrt(0.44*(1-0.44)/50+0.36*(1-0.36)/50)

=0.82

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Step 3: (Find the p-value) = P(Z>0.82) =0.2061 (from standard normal table)

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Step 4: (State the Conclusion in sentence form) Reject/Accept the null hypothesis because