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GarryVolchara [31]
3 years ago
15

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

om 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.
Mathematics
1 answer:
Arturiano [62]3 years ago
7 0

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.

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