Question

2. (12 pts) A random sample of 20 WKU students is collected and the number of credit cards students have is recorded below n 20 0 0 0 0 Construct a 90% confidence interval to predict the number of credit cards that a future WKU student has. Follow the procedure outlined below. ) (6 pts) Check assumptions and determine the apropriate confience interaltous -predict the nvr1ber of credit Sx-1.31C Cards ii) (5 pts) Construct the interval -20 u0 나 Sample random dichn inera

Answer 1

I) Since sample is drawn randomly and independently, assumption for constructing confidence interval is met. The confidence interval is

mu -+ t* sigma / sqrt(n)

Where mu = sample mean

sigma =s standard deviation

n is sample size and t is 90% t value at n= (20-1)= 19 degree of freedom.

Here, mu = 1.55

Sigma = 1.3168

ii) 90% confidence interval is

1.55 -+ 1.729*(1.32/sqrt(20))

1.55 -+ 0.51

(1.04, 2.06)

iii) Thus we are 90% confident that number of credit card that a future WKU student has is between (1.04,2.06).