College Stats Help

Question

You wish to test the following claim (Ha) at a significance level of α=0.002.      

Ho:p=0.73      

Ha:p≠0.73

You obtain a sample of size n=314 in which there are 210 successful observations. 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 = __________

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value = __________

Answer 1

population proportion (p) = 0.73

sample size (n) = 314

x = number of successful observations (210)

mean = n * p = 314 * 0.73 = 229.22

standard deviation (SD) = sqrt(n*p*(1-p)) = sqrt(314*0.73*0.27) = 7.867

z = (x - mean)/SD

z = (210 - 229.22)/7.867 = -2.44

p-value = 2 * P(z < -2.44) = 2* 0.0073 = 0.146.