Question

The heights of a random sample of 100 women are recorded. The sample mean is 65.3 inches and the sample standard deviation is 3 inches. whicho of the following is an approximate 95% confidence interval for the population mean?

A. 65.3 + (2)(0.03)

B. 65.3 + (2)(.3)

C. 65.3 + (2)(3)

D. 65.3 + (2)(30)

Answer 1

Answer: B. $65.3\pm(2)(0.3)$

Step-by-step explanation:

The confidence interval for the population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 100

Sample mean : $\overline{x}=65.3\text{ inches}$

Standard deviation: $\sigma=3 \text{ inches}$

Level of confidence = 0.95

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

Then, 95% confidence interval for the population mean will be :-

$65.3\pm (1.96)\dfrac{3}{\sqrt{100}}\\\\\approx65.3\pm(2)(\dfrac{3}{10})=65.3\pm(2)(0.3)$

Answer 2

Answer:

The answer for this Question is B.

Step-by-step explanation: