A person measures the contents of 36 pop cans and finds the mean content to be 12.1 fluid ounces...

Question:

A person measures the contents of 36 pop cans and finds the mean content to be 12.1 fluid ounces with a standard deviation of 0.2 ounces. The 99% confidence interval for the average fluid content of a can is and you conclude that the population mean is greater than 10.

a.(12.014, 12.186); can

b.(12.014, 12.186); cannot

c.(12.009. 12.191); can

d.(12.009, 12.191); cannot

Confidence Interval:

In this question, we will use the t distribution to construct the 99% confidence interval for the population mean. The t distribution is a sampling distribution with (n-1) degree of freedom. We are using the t distribution because the population standard deviation is unknown.

Answer and Explanation:

Given that,

  • Sample size, {eq}n = 36 {/eq}
  • Sample mean, {eq}\bar{x} = 12.1 {/eq}
  • Sample standard deviation, {eq}s = 0.2 {/eq}


Degree of freedom, {eq}n-1 = 36-1=35 {/eq}


The 99% confidence interval for the population mean is defined as:

{eq}\bar{x} \pm t_{0.01/2}\times \frac{s}{\sqrt{n}} {/eq}


Excel function for the confidence coefficient:

=TINV(0.01,35)


{eq}12.1 \pm 2.724\times \frac{0.2}{\sqrt{36}}\\ 12.009 < \mu < 12.191 {/eq}


The population mean lies outside the confidence interval. So, we reject the null hypothesis.

Therefore, Option (c) is correct.


Learn more about this topic:

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Using the t Distribution to Find Confidence Intervals

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 6
6.2K

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