Question

The “SolJah Grrlz”(Dianaand Gloria) wanted to estimate the difference between the percentages of users of toothpaste who will never switch to toothpaste. They took a sample of 500 users of “Decay Toothpaste” (100 of whomsaid that they would never switch) and 400 users of “Cavity Jamm Paste” (68 of whom said that they would not switch).

a.Construct a 97% confidence interval for the difference between the proportions of all users of the two toothpastes who will never switch. (4pts)

b.Test at the 2%level of significance whether the two population proportions are different. (6pts.)

Answer 1

Explanation

Given first sample proportion

  

Given second sample proportion

97% of confidence intervals for the difference between the proportion is determined by

  

critical values

where

on calculation, we get

97% of confidence intervals for the difference between the proportion of All users of the two tooth pastes who will never switch

  

Lower limit :-

Upper limit :-

97% of confidence intervals for the difference between the proportion of All users of the two tooth pastes who will never switch

b)

Null hypothesis:- H0 :

The two Population proportions are different

Alternative Hypothesis H1 :

The two Population proportions are not different

  

Test statistic

  

where

Test statistic

  

The tabulated value

The calculated value Z = 1.15696 < 2.054 at 0.02 level of significance

Null Hypothesis is accepted at 0.02 level of significance

Conclusion:-

The two Population proportions are different