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

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

Let p₁ and p₂ denote thetrue 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 andp₂:

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

(c) Build a 95% confidence interval for the true decrease inproportion 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 programreduced the amount of spam?

(e) Complete the following to perform a hypothesis test at the5% significance level to test the claim that switching to the newfilter \"Spam-A-Little\" has decreased the proportion of unsolicitedemails 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: