A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 137 ounces and a standard deviation of 0.30 ounces. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 136.9 ounces. Does the machine need to be reset? Explain your reasoning.

Question

09-12-2017
Mathematics

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A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 137 ounces and a standard deviation of 0.30 ounces. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 136.9 ounces. Does the machine need to be reset? Explain your reasoning.

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AlonsoDehner AlonsoDehner · Answer 1 · 2019-03-02T09:28:43+01:00

Answer:

Step-by-step explanation:

Let X be the amount of paint dispensed by a machine used to fill gallon=sized paint cans.

X is Normal(137, 0.30)

Sample size = 45

Sample std error = 0.30/sqrt 45 =0.0447

x bar = 136.9

Create hypotheses as:

H0: sample mean = 137

Ha: sample mean not equal to 137

(Two tailed test)

Test statistic = (136.9-137)/0.0447

=-2.237

p value = 0.0257

Since p >0.01, at 99% level we accept null hypothesis

Machine need not be reset.

andromache andromache · Answer 2 · 2022-03-04T12:48:09+01:00

The machine need not be reset.

Calculation of the machine:

Here we assume X be the amount of paint dispensed by a machine used to fill gallon

Now

X is Normal(137, 0.30)

Sample size = 45

So,

Sample std error = 0.30/sqrt 45 =0.0447

Now

x bar = 136.9

Now we have to Create hypotheses :

H0: sample mean = 137

Ha: sample mean not equal to 137

Now

(Two tailed test)

Test statistic =[tex](136.9-137)\div 0.0447[/tex]

=-2.237

p value = 0.0257

Since p >0.01, at 99% level, so here we accept the null hypothesis.

Therefore, The machine need not be reset.

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