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 $299.4297.7301.0298.9300.2297.0$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 $300ml$? Carry out an appropriate test to support your answer

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 localid="1650344912723" $299.4297.7301.0298.9300.2297.0$

We need to find that the mean amount of cola in all the bottles filled that day differs from the target value of $300ml$localid="1650344915747" $300ml$.

The dataset is

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

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 $300\mathrm{ml}$.