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%**

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