Question

5 It was dcsircd to comparc thc proportion of malcs and fcmalcs that had a tattoo. I cntered the data into Statistix and created the following printout. Two Proportions Hypothesis Test Sample Size Successes Proportion 30900 -0.06800 Difference 31tarrtire Hyp: pl p2 0.03989 SE difference) z uncorrected) 0.0883 L.70 90 Confidence Interval of Difference -0.14619 pl-p2< -0.00238 a. Use the confidence interval to make a statement about the relationship between these two propor 4no softhe problem)? Make sure to include your reliability level in b. Suppose it is desired to reduce the interval width you make to accomplish this goal? (4 points) this problem. What two choices can

Answer 1

a) Given level of significance = 0.10

Since the 90% CI does not contain Zero we conclude that the two proportions are significantly different with a reliability of 91.17% ( 1 - p), We can also conclude that the proportion of females who has tattoo were significantly higher than males who has tattoo. (90% CI is in complete negative range)

b) To decrease the width of CI there are possible ways. i) Increase the sample size ii) Increase the level of significance or decrease the level of confidence.

c) Sample size is large enough in this test. Because np and nq are greater than 10.

for sample i) np = 250 * 0.24 = 60 >10 hence satisfied.

for sample ii) np = 250*03.08 = 77 > 10 hence satisfied.

d) The assumptions required are

i) Samples must be independent

ii) The sample size must be large enough,

which are satisfied in this problem.