Question

A bottle filling process has a setting of 48 ounces which is exactly what consumers want when they buy the vegetable oil. A random sample of 36 bottles produced a sample mean of 48.15 ounces with a standard deviation of 0.3 ounces. Test the hypothesis at the 2% level of significance.

Answer 1

Answer with explanation:

Given : A bottle filling process has a setting of 48 ounces which is exactly what consumers want when they buy the vegetable oil.

Let $\mu$ represents the population mean .

Then, the set of hypothesis will be:-

$H_0: \mu=48$

$H_a:\mu\neq48$ , since the alternative hypothesis is two-tailed , so the hypothesis test is a two-tailed test.

We assume that this is normal distribution.

Sample size : n =36, which is a large sample (z<30) , so we use t-test.

Sample mean : $\overliene{x}=48.15\text{ ounces}$

Standard deviation : $\sigma=0.3\text{ ounces}$

The test statistic for population mean for large sample is given by :-

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

$z=\dfrac{48.15-48}{\dfrac{0.3}{\sqrt{36}}}=3$

The p-value = $2P(z>3)=0.0026998$

Since the p-value is less than the significance level of 0.02 , therefore we reject the null hypothesis and support the alternative hypothesis.

Thus we conclude that we do not have enough evidence to support the claim that a bottle filling process has a setting of 48 ounces which is exactly what consumers want when they buy the vegetable oil.