Question

5. A telephone sales solicitor, trying to decide between two alternative sales pitches, randomly alternated between them during a day of calls. Using approach A, 20% of 100 calls led to requests for the mailing of additional product information. For approach B in another 100 calls, only 14 % led to requests for the product information mailing. At the 0.05 significance level, can we conlcude that the difference in results was due to chance? Construct the 95% confidence level for the difference between population proportions (π1 - π2). Identify and interpret the p-value for the test.

ANSWER FORMAT:

Define H₀ :

Define H₁ :

Test statistic

Critical value of test statistic

Decision rule

Calculated value of test statistic

Reject or fail to reject H₀?

Conclusion about differences in sales pitches

95% confidence interval for difference between proportions

Find the p-value

Interpret p-value

Answer 1

Answer:

Let denoes the proportion of requests for the mailing of additional product information

and denoes the proportion of requests for the product information mailing.

To test against

The test statistic is given by

which under H₀ follows a standard normal distribution.

We reject H₀ if |z_obs|>z_0.025

where

Here

p-value=2*P(Z>1.12946)=0.258704

So,we accept H₀ at 5% level of significance and we can conclude that there is no significant difference between two proportions.

95% confidence interval for π1 - π2

=

=(-0.0441180,0.164118)

Thank you !