Question

1.A particular bank requires a credit score of 640 to get approved for a loan. After taking a sample of 107 customers, the bank finds the 95% confidence interval for the mean credit score is:

662 < μ < 739

Can we be reasonably sure that a majority of people will have a credit score over 640 and be able to get the loan?

• Yes
• No

Why or why not?

2. If n=27, x¯(x-bar)=31, and s=12, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

Answer 1

(A)reasonably sure that a majority of people will have a credit score over 640 and be able to get the loan

yes because  the 95% confidence interval for the mean credit score is fall between the interval

(B)Given that,

= 31

s =12

n =27

Degrees of freedom = df = n - 1 = 27- 1 = 26

a ) At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

t _/2,df = t_0.10, 26 = 1.315

Margin of error = E = t_/2,df * (s /n)

= 1.315* (12 / 27)

=3.04

The 95% confidence interval estimate of the population mean is,

- E < < + E

31 -3.04 < < 31+3.04

28.0 < < 34.0

( 28.0 , 34.0 )