Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu. Assume that the population has a normal distribution.
n=30, x=84.6, s=10.5, 90% confidence
A. 81.36 B. 80.68 C. 79.32 D. 81.34

Answer 1

Answer:

Option A - The population mean is $\mu\approx 81.36$

Confidence interval is (3.153,166.047).

Step-by-step explanation:

Given : Assume that the population has a normal distribution

n=30, x=84.6, s=10.5, 90% confidence.

To find : Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu?

Solution :

First we apply z-score formula,

$z=\frac{x-\mu}{\frac{s}{\sqrt{n}}}$

Where, x is the sample mean x=84.6

s is the standard deviation s=10.5

n is the number of sample n=30

$\mu$ is the population mean

z is the score value, at 90% z=1.645

Substitute all the values in the formula,

$1.645=\frac{84.6-\mu}{\frac{10.5}{\sqrt{30}}}$

$1.645\times \frac{10.5}{\sqrt{30}}=84.6-\mu$    

$1.645\times 1.917=84.6-\mu$    

$3.153=84.6-\mu$    

$\mu=84.6-3.153$    

$\mu=81.447$    

So, The population mean is $\mu=81.447$

Therefore, Option A is correct.

Now, Apply confidence interval formula

$x-\mu<CI<x+\mu$

$84.6-81.447<CI<84.6+81.447$

$3.153<CI<84.6+166.047$

Therefore, Confidence interval is (3.153,166.047).