Question

NYU is testing out two different versions of filtering software in order to reduce spam emails. The old version is called "Spam-A-Lot" and the new version is called "Spam-A-Little." In testing each version of the software the following data was produced:

Email Account	Solicited Mail	Unsolicited Mail	TOTAL
Spam-A-Lot	305	95	400
Spam-A-Little	150	38	188

Let p₁ and p₂ denote the true proportion of unsolicited mail that make it through the "Spam-A-Lot" and "Spam-A-Little" filters, respectively.

(a) Determine the unbiased point estimates of p₁ and p₂:

(b) Explain why the formula for a large-sample confidence interval estimate for p1 - p2 can be used in this case.

(c) Build a 95% confidence interval for the true decrease in proportion p1 - p2 of unsolicited mail by switching filters from "Spam-A-Lot" (p₁) to "Spam-A-Little" (p₂), using the sample values given. Record results to 4 decimals.

(d) Based on your answer to (c), has the new filtering program reduced the amount of spam?

(e) Complete the following to perform a hypothesis test at the 5% significance level to test the claim that switching to the new filter "Spam-A-Little" has decreased the proportion of unsolicited emails getting through the filter.

i) H₀:

H_a:

Level of Significance:

Observed Test Statistic (z-statistic):

ii) p-value:

Decision with justification:

Conclusion in context:

Answer 1

(a)

(b)

Since sample sizes are large and number of successes and failuers are greater than 5 so we can use the formula for a large-sample confidence interval estimate for p1 - p2.

(c)

(d)

Since confidence interval contains zero so we cannot conclude that the new filtering program reduced the amount of spam.

(e)

Conlusion: There is no evidence to conclude that the new filtering program reduced the amount of spam.