In: Statistics and Probability
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.
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Interpret the interval in this context.
Does the confidence interval provide evidence that contributions are different between email and the telephone contact?
If you ran a TEST on your calculator, please tell me what TEST you ran here
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,