It was desired to compare the proportion of males and females that had a tattoo. I entered the data into Statistix and created the following printout.
Hypothesis Test - Two Proportions
Sample
Size Successes Proportion
Males 350 100 0.28571
Females 350 130 0.37143
Difference -0.08571
Null Hypothesis: p1 = p2
Alternative Hyp: p1 ≠ p2
SE (difference) 0.03551
Z (uncorrected) 2.41 P 0.0158
95% Confidence Interval of Difference
-0.15501 < p1-p2 < -.01642
a. What can you say about the relationship between these two proportions (in the words of the problem)? Make sure to include your reliability level in your answer. (4 points)
We are 95% confident that the proportion of all males with a tattoo is less than the proportion of all females with a tattoo.
b. Suppose it is desired to reduce the interval width in this problem. What two choices can you make to accomplish this goal? (4 points)
-Increase sample size.
-Lower the confidence level.
c. Is the sample size considered large in this problem? Why or why not? (4 points).
Correct answer, rule, and calculation.
Yes, because np ³ 5 and nq ³ 5.
np = (350) *(0.0158) = 5.53
nq= (350) *(1-0.0158) = 344.47