Question

The contents of 3838 cans of Coke have a mean of x¯¯¯=12.15x¯=12.15. Assume the contents of cans of Coke have a normal distribution with standard deviation of σ=0.12.σ=0.12. Find the value of the test statistic zz for the claim that the population mean is μ=12.μ=12.

Answer 1

Answer: 7.7055

Step-by-step explanation:

Given: Sample size : $n= 38> 30\text{ i.e. Large sample}$

Sample Mean : $\overline{x}=12.15$

Standard deviation : $\sigma =0.12$

Claim : The population mean is $\mu=12$

We assume the contents of cans of Coke have a normal distribution .

We know that the test-static for population mean for larger sample is given by :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow z=\dfrac{12.15-12}{\dfrac{0.12}{\sqrt{38}}}=7.70551750371\approx7.7055$

Hence, the value of the test statistic z for the claim that the population mean is μ=12 is 7.7055.