Question

Section 6.2 (10 points) 1) A marketing survey involves product recognition in New York and California. 259 out of 558 New Yorkers surveyed knew of the product, while 191 out of 614 Californians knew of the product. a) Construct a 99% confidence interval for the difference between the two population proportions. Assume all necessary conditions have been met! b) Does the interval computed above lead you to think that there is a statistically significant difference between the two population proportions? Circle one: Yes No c) Explain how you came to your decision in part b using the 99% confidence interval you computed in part a for the difference between the two population proportions:

Answer 1

Answer

(A) given that

x1 = 259

n2 = 558

x2 = 191

n2 = 614

confidence level is 99%

Using TI 84 calculator

press stat then tests then 2-PropZtest

enter the given data values

then press calculate, we get

Lower limit = 0.080

upper limit = 0.226

(B)

Yes, interval computed above lead us to think that there is a statistically significant difference between the two population proportions

(C) We can see that the lower limit for the confidence interval is above 0, this means that the confidence interval for proportion difference is above 0

therefore, there is a statistically significant difference between the two population proportions as the 0 value is not included in confidence interval