SOLUTION: Your sample consists of 72 subjects, with 53 successes. Calculate the test statistic, rounded to 2 decimal places. H0:p=0.69 H1<0.69

Algebra ->  Probability-and-statistics -> SOLUTION: Your sample consists of 72 subjects, with 53 successes. Calculate the test statistic, rounded to 2 decimal places. H0:p=0.69 H1<0.69      Log On


   

Question 1160720: Your sample consists of 72 subjects, with 53 successes. Calculate the test statistic, rounded to 2 decimal places. H0:p=0.69 H1<0.69
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

n = 72 is the sample size
x = 53 is the number of successes
phat = x/n = 53/72 = 0.736111 is the approximate sample proportion
p = 0.69 is the hypothesized population proportion

Calculate the standard error (SE)
SE = sqrt(p*(1-p)/n)
SE = sqrt(0.69*(1-0.69)/72)
SE = 0.054505 which is approximate

Use the values of phat,p and SE to find the z test statistic
z = (phat - p)/SE
z = (0.736111 - 0.69)/0.054505
z = 0.845996 also approximate
z = 0.85 rounding to two decimal places

Answer: z = 0.85