Question

c. Draw a graph to display both confidence intervals. smaller O A larger B. 96% CI for 99% CI for 99% CI for 95% CI for 7.5 5.5 O c. Q OD. 96% CI for 95% CI for 99% CI for 99% CI for 7.5 5.5 d. Which confidence interval yields a more accurate estimate of u? Explain your answer. The 95% confidence interval is a more accurate estimate, because it is narrower than the 99% confidence interval.

Answer 1

n = 10, $\sigma$ = 2.02. Let random variable X denote the investment ina firm. Given $\sum X_i$ = 57.42. Hence,

X = ΣΧ/n = 57.42/10 = 5.742

a.z value = 2.58.

99% C.I. is: $\small (\bar X - z*\sigma/\sqrt{n}, \bar X + z*\sigma/\sqrt{n}) = (5.742 - 2.58*2.02/\sqrt{10}, 5.742 + 2.58*2.02/\sqrt{10})$

(4.09, 7.39)

b.The 99% confidence inerval is longer than the 95% confidence interval because the 99% C.I. has a higher probability (99% probability) that the mean is contained within it.

Other part of the question is:

Compared to the 95% confidence interval, the value of  $\small Z_{\alpha/2}$ is larger in the 99% confidence interval.

c.Answer is A.

d.99% confidence interval gives a more accurate estimate than the 95% confidence interval because the 99% C.I> has a higher chance the the population mean is contained within it. Even though the 95% C.I, is narrower, it has a smaller probability that the mean is inside it.