4) A researcher wants to find if women or men are more likely to enjoy roller co

Question

4) A researcher wants to find if women or men are more likely to enjoy roller coasters. She asked 40 women and 35 men the following question, "Do you like roller coasters?" 31 of the women responded, 'yes', and 21 of the men responded, 'yes'. Can the researcher conclude at the .05 level of significance that there is a difference in the proportion of women who like roller coasters and the proportion of men that like roller coasters? Show all 5 steps. (10 Points) 5) For Problem #4, calculate the p-value. (5 Points)

Explanation / Answer

4)
Ho : p1 =p2
Ha: p1 =/ p2

Test and CI for Two Proportions

Sample   X   N Sample p
1       31 40 0.775000
2       21 35 0.600000

Difference = p (1) - p (2)
Estimate for difference: 0.175
95% CI for difference: (-0.0325760, 0.382576)
Test for difference = 0 (vs 0): Z = 1.64 P-Value = 0.101

TS = 1.64

critical value = 1.96
since TS< critical value
we fail to reject the null hypothesis

5)
p-value = 2 P( Z > 1.64) = 0.101

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