Question

A researcher wants to estimate the difference between the proportions of users of two shampoos who are satisfied with the product. In a sample of 400 users of Fancy Pants Shampoo taken by this researcher, 78 said they are satisfied. In another sample of 500 users of Smooth Operator Shampoo taken by the same researcher, 92 said they were satisfied.

We are going to test if we can conclude that the proportion of Fancy Pants users who are satisfied is different from the proportion of Smooth Operator users who are satisfied with the product.

a. Define the relevant parameters and state the hypotheses. [3pts]

b. Find the observed sample statistic, pooled proportion, and the test statistic. Use proper notation for the sample statistic ( x or p ˆ ), and clearly identify your test statistic as either a z-score or a t-score. [4pts]

c. Find the p-value of your test statistic. You are required to graph the test statistic on its corresponding distribution, shade the appropriate area, and provide correct calculator documentation. Box final answer. [3pts]

d. Make a generic decision about H0 . [2pts]

f. Make a conclusion in the context of the problem. [2pts]

g. Construct a 99% confidence interval for the difference between proportion of Fancy Pants users and Smooth Operator users who are satisfied with the product. [5 pts]

h. Provide an interpretation of your interval in the context of the data. [2pts]

Answer 1

Anvier from the given cheta. Р. 18 400 -0.195 42 500 0184 P₂ N 78442 0.1889 P - Yoo + 500 ve 0.01 The hypothesis are H-P.-P2 Ha= P&P, Rejection region (Ⓡ) (7:171 72.58ý Z- 0-195 - 0.184 O=0.419 Vro-1) Vojt "ma) Jo-189. (1-0-187) ('foot "soc) 121 -0.418 € 2 - 2.58. P = 0.6753, since Pr 0.6753 Zo of It is concluded that the null hypothesis is not rejected is not rejected, P, is ditferent than P, at the 0.01 significance level. At the confidence interval P-P2 is 991. C.I -0.057 LP, P2² 20.079. H.