Question

Pill. IUU lave used a Gas LULU 11. Due in 5 hours, 17 minutes. Due Fri 05/01/2020 11:59 pm You wish to test the following claim (1.) at a significance level of a = 0.001. H:P1 = P2 H:P.<P2 You obtain 71.8% successes in a sample of size Thy = 628 from the first population. You obtain 79.5% successes in a sample of size 7 = 381 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic U What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is. less than or equal to) a greater than a This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion. The sample data support the claim that the first population proportion is less than the second population proportion There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.

Answer 1

Solution :

Ho : p1 = p2

Ha : p1 < p2

α = 0.001

n1 = 628 , n2 = 381 , p1^ = 0.718 , p2^ = 0.795

p bar = (n1p1^ + n2p2^)/(n1+n2) , q bar = 1 - p bar

Test Statistic Z = (p1^ - p2^) / SQRT(((p bar * q bar)/n1)+((p bar * q bar)/n2)

= -2.73

test statistic = -2.73

p value = P ( z < -2.73)

= NORMSDIST(-2.73) = 0.0032 ( Using excel function )

p value = 0.0032

p value is

• greater than α

The test statistic lead to decision to,..

• Fail to reject null

• There is not sufficient sample evidence to support the claim that the first population proportion less than the second population proportion.