Question

Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of 3 ml. A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4 297.7 301.0 298.9 300.2 297.0 Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? Test at the 5% significance level.

Answer 1

Answer:

We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

Step-by-step explanation:

We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.

A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0

Let $\mu$ = mean contents of cola bottles.

SO, Null Hypothesis, $H_0$ : $\mu \geq$  300 ml   {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}

Alternate Hypothesis, $H_A$ : $\mu$ < 300 ml   {means that the mean contents of cola bottles is less than the advertised 300 ml}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

                       T.S.  = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\bar X$ = sample mean contents of cola bottle = $\frac{\sum X}{n}$ = 299.03 ml

            $\sigma$ = population standard deviation = 3 ml

            n = sample of bottles = 6

So, test statistics  =  $\frac{299.03-300}{\frac{3}{\sqrt{6} } }$     

                               =  -0.792

Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.