Question

According to a survey in a​ country, 3636​% of adults do not own a credit card. Suppose a simple random sample of 400400 adults is obtained.

-Would it be unusual for a random sample of 400 adults to result in 136 or fewer who do not own a credit​ card? Why? Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as​ needed.)

a) The result is unusual because the probability that p hat is less than or equal to the sample proportion is ___ which is greater than 5%

b) The result is not unusual because the probability that p hat is less than or equal to the sample proportion is ____ which is less than 5%

c) The result is unusual because the probability that p hat is less than or equal to the sample proportion is ___ which is less than 5%

d) The result is not unusual because the probability that p hat is less than or equal to the sample proportion is ___ which is greater than 5%

Answer 1

Ho: po <= .36
h1: po > .36

X=   136  
n=   400  
p-hat = X/n=   0.340    =136/400
po=   0.360   

test statistic, z = (phat-p)/sqrt(p*(1-p)/n)
z = (0.34-0.36)/SQRT(0.36*(1-0.36)/400)
z = -0.833

p-value = 1-P(Z<z)
p-value = 1-P(z<-0.833333)
p-value = 1-NORMSDIST(-0.833333)
p-value = 0.79767

Since p>5%, i fail to reject ho and conclude that p<=0.36

hence the correct option is :

d) The result is not unusual because the probability that p hat is less than or equal to the sample proportion is __0.7977_ which is greater than 5%