Data 606 Chapter 4 Presentation

4.45

Spam mail percentages. The National Technology Readiness Survey sponsored by the Smith School of Business at the University of Maryland surveyed 418 randomly sampled Americans, asking them how often they delete spam emails. In 2004, 23% of the respondents said they delete their spam mail once a month or less, and in 2009 this value was 16%.

A. What are the hypotheses for evaluating if the proportion of those who delete their email once a month or less has changed from 2004 to 2009?

H~O: There is no difference in how Americans deleted their emails in 2004 versus 2009 \[P_{email2004}=P_{email2009}\] H~A: There is a difference in how often Americans deleted their emails in 2004 versus 2009 \[P_{email2004} \neq P_{email2009}\]

B. What is the point estimate for the difference between the two population proportions?

• Our hypothesis test states that the difference between the sample means should be 0.
• The point estimate is the difference between the sample mean

P2009<- 16
P2004 <- 23
P2009-P2004

## [1] -7

• Our point estimate is -7

C. A report on the survey states that the observed decrease from 2004 to 2009 is statistically significant. Explain what this means in context of the hypothesis test and the data

• Assuming they used a 95% significance level, this means that there is at least a 95% likelihood that the true proportion of people that deleted emails in 2009 was lower than in 2004. This means we can reject our null hypothesis, and state that there is an actual difference or a non-random sampling difference between the rate at which people deleted emails in 2004 and in 2009.

Example of what our Confidence interval may look like

D. Would you expect a confidence interval for the difference between the two population proportions to contain 0? Explain your reasoning.

• As shown above, no. If our confidence interval contains 0 then we would have accepted the null hypothesis and concluded that the difference could be attributed to random sampling