Mathematics, 13.03.2020 03:58 maceyshaynee9507

A machine that puts corn flakes into boxes is adjusted to put an average of 15.6 ounces into each box, with standard deviation of 0.26 ounce. If a random sample of 15 boxes gave a sample standard deviation of 0.39 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment

Answers: 1

Show answers

Answers

Answer from: Coltong121

$\chi^2 =\frac{15-1}{0.0676} 0.1521 =31.5$

$p_v =P(\chi^2_{14} 31.5)=0.0047$

If we compare the p value and the significance level assumed of 0.05 we see that p_v so on this case we have enough evidence in order to reject the null hypothesis at the significance level provided. And that means that the population variance is significantly higher than 0.26^2=0.0676.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

n=15 represent the sample size

$\alpha$ represent the confidence level

s^2 =0.39^2 =0.1521 represent the sample variance obtained

$\sigma^2_0 =0.26^2 =0.0676$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is violated, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \leq 0.0676$

Alternative hypothesis: $\sigma^2 0.0676$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{15-1}{0.0676} 0.1521 =31.5$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case df=15-1=14. And since is a right tailed test the p value would be given by:

$p_v =P(\chi^2_{14} 31.5)=0.0047$

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(31.5,14,TRUE)"

Conclusion

Answer from: Quest

Your maths is very weak try yourself this would improve your skills don't depend on others

Answer from: Quest

the 4th choice is the correct one

step-by-step explanation:

*sigh* i seriously need on this question. i don't understand it. i would appreciate it if somebody

Another question on Mathematics

Mathematics, 21.06.2019 19:10

Labc is reflected across x = 1 and y = -3. what are the coordinates of the reflection image of a after both reflections?

Answers: 3

Answer

Mathematics, 22.06.2019 01:00

1) your friend taylor missed class today and needs some identifying solutions of systems. explain to taylor where to find the solution(s) of any system using its graph 2)taylor graphs the following in desmos and decides that f(x) = g(x) at x = 0, x = 1, & x = 3. f(x) = 2x+1g(x) = 2x2+1 provide taylor some feedback that explains which part of the answer was incorrect and why.

Answers: 1

Answer

Mathematics, 22.06.2019 05:00

At saturday nights football game there were 18 less fans than half the fans at friday nights game.there were "x" fans at friday's game.write an expression to represent the number of fans at saturday's game. *** urgent***

Answers: 3

Answer

Mathematics, 22.06.2019 05:00

If you apply the changes below to the linear parent function .f(x)=x what is the equation of the new function ? vertically stretch by a factor of 3 ; flip over the x axis

Answers: 3

Answer

You know the right answer?

A machine that puts corn flakes into boxes is adjusted to put an average of 15.6 ounces into each bo...

Questions