In San Francisco, a sample of 3,153 wireless routers showed that 1,104 used encr

Question

In San Francisco, a sample of 3,153 wireless routers showed that 1,104 used encryption (to prevent hackers from intercepting information). In Seattle, a sample of 1,860 wireless routers showed that 625 used encryption.

(a) Choose the appropriate hypotheses to test whether or not the population proportion of encryption is higher in San Francisco than Seattle. Assume 1 is the proportion for San Francisco and 2 for Seattle.

a. H0: 1 2 0 vs. H1: 1 2 > 0.

b. H0: 1 2 0 vs. H1: 1 2 0.

(b-1) Specify the decision rule at = .10. (Round your answer to 3 decimal places.)

Reject the null hypothesis if zcalc > .

(b-2) Find the test statistic zcalc. (Do not round the intermediate calculations and round x1 and x2 to the nearest whole number. Round your answer to 3 decimal places.)

zcalc            

(b-3) Choose the correct conclusion.

We (do not reject or reject) the null hypothesis.

Explanation / Answer

The correct hypothesis is A.  H0: 1 2 0 vs. H1: 1 2 > 0

b-2 and b-3) The Z-Score is 1.0161. The p-value is 0.15386. The result is not significant at p <0.10. The proportion of Yes or No responses for Observation 1 is 0.35. The proportion for Observation 2 is 0.336.

b-1) Z-critical is 1.28 for alha=0.10

b-3) We do not reject the null hypothesis.

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