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Andrews [41]
3 years ago
11

The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30

bottles showed a standard deviation of .2. The p-value for the test is _____.
a. .025
b. between .025 and .05
c. .05
d. between .05 and .01
Mathematics
1 answer:
o-na [289]3 years ago
6 0

Answer:

p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459

b. between .025 and .05

Step-by-step explanation:

Previous concepts and notation

The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".

\bar X represent the sample mean

n = 30 sample size

s= 0.2 represent the sample deviation

\sigma_o =\sqrt{0.027}=0.164 the value that we want to test

p_v represent the p value for the test

t represent the statistic

\alpha= significance level

State the null and alternative hypothesis

On this case we want to check if the population standard deviation is less than 0.027, so the system of hypothesis are:

H0: \sigma \leq 0.027

H1: \sigma >0.027

In order to check the hypothesis we need to calculate the statistic given by the following formula:

t=(n-1) [\frac{s}{\sigma_o}]^2

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

t=(30-1) [\frac{0.2}{0.164}]^2 =42.963

What is the approximate p-value of the test?

The degrees of freedom are given by:

df=n-1= 30-1=29

For this case since we have a right tailed test the p value is given by:

p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459

And the best option would be:

b. between .025 and .05

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*See the attachment below.

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