Q.80 - The Practice of Statistics for AP

Question

Bottles of a popular cola are supposed to contain $300$ milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day’s production. The results are $299.4 297.7 301.0 298.9 300.2 297.0$ Do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day differs from the target value of $300 ml$? Carry out an appropriate test to support your answer 

Step-by-Step Solution

Answer

Subsequently, at $5\%$  significance level there is insufficient evidence to conclude that average amount of cola that is filled in bottle is different from $300\mathrm{ml}$.

Step 1: Given information

Given in the question that,  Bottles of a popular cola are supposed to contain $300$ milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day’s production. The results are $299.4 297.7 301.0 298.9 300.2 297.0$

We need to find  that the mean amount of cola in all the bottles filled that day differs from the target value of $300 ml$$300 ml$.

Step 2: Explanation

The dataset is

$299.4$

$297.7$

$301$

$298.9$

$300.2$

$297$

The test statistic is computed as:

$t=\frac{\overline{x}-\mu }{\frac{x}{\sqrt{n}}}$

Here,

$\overline{x}=$ Sample mean

$\mu =$ Population mean

$n=$Sample size

$s=$ Sample standard deviation

Step 3: Null and alternative hypotheses

Here, 

$\mu$- Be the average amount of cola that is filled in bottle.

The null and alternative hypotheses are:

$H_0:\mu =300$

$H_a:\mu \ne 300$

The obtained excel output is:

Assume level of significance to be $0.05$.

Here,

 p-value is$0.1760$.

Here, p-value > level of significance. Thus, the decision is not to reject the null hypothesis.

Subsequently, at $5\%$ significance level there is insufficient evidence to conclude that average amount of cola that is filled in bottle is different from $300\mathrm{ml}$.