# Given a random sample of 49 objects with mean 12 and variance 4, give a 95% Cl for the population...

## Question:

Given a random sample of 49 objects with mean 12 and variance 4, give a 95% Cl for the population mean. Assume the population is normal.

## Confidence Interval:

In this question, we will use the t distribution to calculate and construct the 95% confidence interval for the population mean. A confidence interval provides the lower and the upper limits of a population parameter.

## Answer and Explanation:

Given that,

• Sample size, {eq}n = 49 {/eq}
• Sample mean, {eq}\bar{x} = 12 {/eq}
• Sample variance, {eq}s^2 = 4 {/eq}

Degree of freedom, {eq}n-1 = 49 - 1 = 48 {/eq}

The 95% confidence interval for the population mean is defined as:

{eq}\bar{x} \pm t_{0.05/2}\times \frac{s}{\sqrt{n}} {/eq}

Excel function for the confidence coefficient:

=TINV(0.05,48)

{eq}12 \pm 2.0106\times \frac{2}{\sqrt{49}}\\ 11.4255 < \mu < 12.574 {/eq}

#### Learn more about this topic: Using the t Distribution to Find Confidence Intervals

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 6
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