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

The answer for this Question is B.

Explanation:

Answer 2

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

Explanation:

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

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(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)(3)/(√(100))\\\\\approx65.3\pm(2)((3)/(10))=65.3\pm(2)(0.3)`