Question

(1 point) Credit scores are used by banks, financial institutions, and retailers to determine one's trustworthiness, and their ability to pay their credit card, when he/she is given a credit card. The higher the credit score, the better the credit (and the more financially trustworthy) a consumer is. In light of the current economic downtur, an economist claims that the credit score of Canadians between the ages of 25 to 40 has remained the same. Prior to the current economic downturn, the mean credit score for Canadians between the ages of 25 to 40 was 670. A random sample of 20 Canadians between the ages of 25 to 40 was taken the mean was found to be 600, with a standard deviation of 37 (a) Choose the correct statistical hypotheses A B : 2 670, H: 670 B. H: X > 670, HA: X < 670 6. Hp : 670, FA: 44 670 D. H.: 670H : < 670 E. H. :X-670, HA: X 670 . F. H: 670, 670 (b) Find a 4 confidence interval for pl. Use at least 4 digits after the deomial if rounding Minimum lower bound when -69 Maximum upper bound when a 6% (c) The sampling distribution used to calculate the confidence interval in part (b) follows a Student's T distribution with degrees of freedom 19 (d) Conducting your statistical testata 6%, you should not reject the nul hypothesis One can conclude from this sample that the mean credit score s similar to 670 Preview My Answers Submit Awers

Answer 1

(a)

Correct option:

F     H0: $\mu$ =670. HA:   $\mu \neq$ 670

(b)

$\alpha$ = 0.06

n = 20

$\bar{x}$ = 669

s = 37

SE = s/$\sqrt{n}$

= 37/$\sqrt{20}$

8.2735

ndf = 20- 1 =19

From Table, critical values of t = $\pm$ 2.00

Confidence Interval:

669 $\pm$ (2.00 X 8.2735)

= 669 $\pm$ 16.547

= ( 652.453 ,685.547)

Confidence Interval:

652.453 <   $\mu$    <    685.547

So,

Answer is:
minimum lower bound = 652.453 when $\alpha$ = 6%

maximum lower bound = 685.547 when $\alpha$ = 6%

(c)

Correct option:
Student's t distribution with degrees of freedom 19

(d)

Correct option:

not reject

One can conclude from this sample that the mean credit score is similar to 670.