Question

Billy-Bob thinks that Pepsi is cheating him! He bought 36 cans of Pepsi and found the mean amount of soda to be 11.79 ounces with a standard deviation of 0.21. Make a 95% confidence interval for the mean amount of soda in each can. Is Pepsi filling the cans with less than 12 ounces of soda?

Answer 1

Given:

Number of cans he bought = 36

mean = 11.29

standard deviation = 0.21

The confidence interval (C.I) can be found using the formula:

$\begin{gathered} CI\bar{=x}\text{ }\pm\text{ z}\frac{s}{\sqrt[]{n}} \\ Where \\ \bar{}x\text{ is the mean} \\ z\text{ is the z-score at the given confidence level} \\ s\text{ is the standard devaition} \\ n\text{ is the sample size} \end{gathered}$

The z-score at 95% confidence level is 1.960

Substituting the given values into the formula:

$\begin{gathered} CI\text{ = 11. 79 }\pm\text{ 1.96 }\times\text{ }\frac{0.21}{\sqrt[]{36}} \\ =\text{ 11.79 }\pm\text{ 0.0686} \\ =\text{ (11.7214, 11.8586)} \end{gathered}$

Answer:

Confidence interval : (11.7214, 11.8586)

Is pepsi filling the cans with less than 12 ounces of soda?

From the confidence interval, we can be 95% certian that the population mean lies in the range (11.7214, 11.8586).

Yes, Pepsi is filling cans with less than 12 ounces of soda