This Question: 1 pt 3of15(0complete) This Quiz: 15 pts possible Question Help *

Question

This Question: 1 pt 3of15(0complete) This Quiz: 15 pts possible Question Help * se A random sample of 15 colleges was taken. The mean debt after graduation was $18,792 with a margin of eror of $1157. The distribution of debt is Normal. Complote parts (a) and (b) below S6 a. Choose the correct interpretation of the confidenoe interval below and fil in the answer boxes to complete your choice. Type whole numbers. Use ascending order.) OA. we are 95% confident that the population mean is between SMI and s1 OR, we are 95% confident that the sample mean is between Sand oc. we are 95% confident that the boundaries for the interval are Sand se S. b. Can we reject a population mean of $18,463 on the basis of these numbers? Explain A. Yes, reject $18,463. Since $18,463 is in the interval, is not plausible the population mean student debt is S 18,463. O B. No, do not reject $18,463. Since S1 8,463 is not in the interval, it is plausible the population mean student debt is S 18,463. ° C. Yes, reject S 18.463. Since S 18463 is not ithe interval, it is not plausible the population mean student debt is $18,463. 0 D. No, do not reject $18,463. Since S 18,463 s in the interval, it is plausible the population mean student debt is $18,463 O E. There is insufficient information to make a decision regarding the rejection of $18.463. The sample size of 15 colleges is less than the required 25 Click to select your answer 29

Explanation / Answer

1)A) The confidence interval is

Mean +/- margin of error

= 18792 +/- 1157

= 17635, 19949

Option-A) we are 95% confidence that the population mean is between 17635 and 19949

B) Option-D

2) mean = (10.6 + 10.6 + 10.8 + 10.2)/4 = 10.55

Variance = ((10.6 - 10.55)^2 + (10.6 - 10.55)^2 + (10.8 - 10.55)^2 + (10.2 - 10.55)^2)/4 = 0.0475

Standard deviation = sqrt (0.0475) = 0.2179

The confidence interval is

Mean +/- z* * sd/sqrt (n )

= 10.55 +/- 1.96 * 0.2179/sqrt(4)

= 10.55 +/- 0.214

= 10.337, 10.764

Option-C is the correct answer.

B) Option-A

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