Question

In: Statistics and Probability

A nonprofit organization appeals for donations by phoning or emailing recent college graduates. A random sample...

A nonprofit organization appeals for donations by phoning or emailing recent college graduates. A random sample of 300 graduates shows that 40% of the 150 who were contacted by telephone actually made contributions compared to only 30% of the 150 who received email requests.

Calculate a 95% confidence interval for the difference in the proportions of graduates who may make donations if contacted by phone or by email. Give your answer to at least 4 decimal places.

(,)

  1. Interpret the interval in this context.

  2. Does the confidence interval provide evidence that contributions are different between email and the telephone contact?

  3. If you ran a TEST on your calculator, please tell me what TEST you ran here

Solutions

Expert Solution

using excel>Addin>phstat>two sample test

we have

Z Test for Differences in Two Proportions
Data Confidence Interval Estimate
Hypothesized Difference 0 of the Difference Between Two Proportions
Level of Significance 0.05
Group 1 Data
Number of Items of Interest 60 Confidence Level 95%
Sample Size 150
Group 2 Intermediate Calculations
Number of Items of Interest 45 Z Value -1.959963985
Sample Size 150 Std. Error of the Diff. between two Proportions 0.054772256
Interval Half Width 0.107351649
Intermediate Calculations
Group 1 Proportion 0.4 Confidence Interval
Group 2 Proportion 0.3 Interval Lower Limit -0.007351649
Difference in Two Proportions 0.1 Interval Upper Limit 0.207351649
Average Proportion 0.35
Z Test Statistic 1.815682598
Two-Tail Test
Lower Critical Value -1.959963985
Upper Critical Value 1.959963985
p-Value 0.069419075
Do not reject the null hypothesis

we will use z test for difference in two proportion

a 95% confidence interval for the difference in the proportions of graduates who may make donations if contacted by phone or by email is (-0.0074,0.2074)

we are 95% confident that the  difference in the proportions of graduates who may make donations if contacted by phone or by email lies in between (-0.0074,0.2074)

No , the confidence interval not  provides evidence that contributions are different between email and the telephone contact,


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