Answer Happy

(9.1) A researcher wants to study the difference between the percentages of users of two toothpastes who will never switch to another toothpaste. In a sample of 500 users of Toothpaste A, 100 said that they will never switch to another toothpaste. In another sample of 400 users of Toothpaste B, 68 said that they will never switch to another toothpaste. Let P1 be the true population proportion of users of Toothpaste A who will never switch to another toothpaste P2 be the true population proportion of users of Toothpaste B who will never switch to another toothpaste (a) (2 pts) What is the point estimate for P1 - P2? (b) (6 pts) Construct a 99% confidence interval for P1 - P2. (c) (5 pts) Interpret the confidence interval computed in (b). (d) Perform a hypothesis test to test the claim: Proportion of users of Toothpaste A who will never switch to another toothpaste is higher than the proportion of users of Toothpaste B who will never switch to another toothpaste. (i) (4 pts) Formulate the null and alternative hypotheses. Consider the following StatCrunch output related to this study. Options 50 x Two sample proportion summary hypothesis test: P1 : proportion of successes for population 1 P2 : proportion of successes for population 2 Pi-P2 : Difference in proportions Hypothesis test results: Difference Counti Totali Count2 Total2 Sample Diff. Std. Err. Z-Stat Pi - P2 100 500 68 400 0.03 0.026138095 1.1477501 P-value 0.1255

(ii) (4 pts) What is the computed test statistic assuming the null hypothesis Ho is true. (iii) (4 pts) identify P-value (iii) (5 pts) At a=0.01 level of significance, state your conclusion in the context of this study.