Explain whether we can use the z test for a proportion in these situations. (a)

Question

Explain whether we can use the z test for a proportion in these situations. (a) You toss a coin 12 times in order to test the hypothesis Ho: = 0.5 that the coin is balanced The sample size 12 is too small The sample size 12 is too large. We cannot be certain that the coin is balanced A z-test for a proportion can be used (b) A local candidate contacts an SRS of 900 of the registered voters in his district to see if there is evidence that more than half support the bill he is sponsoring The sample size 900 is too large. The expected number of 'no' responses is too small: n(1-po) = 900(0.5) = 450. The sample size 900 is too small. A z-test for a proportion can be used. (c) A college president says, "99% of the alumni support my firing of Coach Boggs." You contact an SRS of 400 of the college's 15,000 living alumni to test the hypothesis Ho: 0.99 The sample size 400 is too small. The expected number of 'no' responses is too small: n(1-po) = 400(0.01) = 4. The sample size 400 is too large. A z-test for a proportion can be used

Explanation / Answer

(a) the sample size 12 is too small

Note : np and n(1-p) should be greater than or equal to 10

Here np = 12* 0.5= 6 and n(1-p) = 6

(b) a z test for proportion can be used

note: np = 450 > 10 and n(1-p) = 450

(c) the expected number of no responses is too small n(1-p) = 4 < 10

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