Question 1

In a sample of n = 25 selected from a normally distributed population,we find a population variance of s² = 150.What is the value of χ² if we are testing H₀: σ² = 100?

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Question 2

In a sample of n = 16 selected from a normally distributed population,we find a population standard deviation of s = 10.What are the degrees of freedom for the hypothesis test?

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The answer of In a sample of n = 16...

Question 3

Given the following information about a hypothesis test of the difference between two variances based on independent random samples,what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations. $H _ { A } : \sigma ^ { 2 } A > \sigma ^ { 2 } B , \bar { X } _ { 1 } = 12 , \bar { X } _ { 2 } = 9 , s _ { 1 } = 5 , s _ { 2 } = 3 , n _ { 1 } = 13 , n _ { 2 } = 10$

Accepted Answer

The test statistic for testing the difference between two variances based on independent random samples follows the F-distribution.

The formula for the test statistic is:

F = (s1^2 / s2^2)

Where s1^2 is the sample variance of sample 1, and s2^2 is the sample variance of sample 2.

The critical value of the test statistic at a significance level of .05 can be obtained from an F-table with degrees of freedom df1 = n1-1 (for sample 1) and df2 = n2-1 (for sample 2).

Using the values given in the problem, we get:

F = (5^2/3^2) = 8.33

df1 = 13-1 = 12

df2 = 10-1 = 9

Looking at the F-table, with df1 = 12 and df2 = 9, at a significance level of .05, the critical value is 3.07.

Therefore, the best choice is C) 3.07.

Question 4

Two independent samples selected from two normally distributed populations have variances of σ₁² and σ₂² with n₁ = 10 and n₂ = 15.The degrees of freedom for the F distribution when testing the equality of the two population variances are:

Accepted Answer

The degrees of freedom for the F distribution when testing the equality of two population variances are (n1-1, n2-1), which in this case is (10-1, 15-1) = (9, 14). Therefore, the best choice is C.

Question 5

A manufacturer of an automobile part has a process that is designed to produce the part with a target of 2.5 inches in length.In the past,the standard deviation of the length has been 0.035 inches.In an effort to reduce the variation in the process,the manufacturer has redesigned the process.A sample of 25 parts produced under the new process shows a sample standard deviation of 0.025 inches.Test the claim that the new process standard deviation has improved from the current process at α = .05.

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Question 6

Testing H₀: σ₁² = σ₁²,H_A: σ₁² > σ₂² at α = .01,where n₁ = 5,n₂ = 6,s₁² = 15,750,and s₂² = 10,920,can we reject the null hypothesis?

Accepted Answer

The answer of Testing H₀: σ₁² = σ₁²,H_A: σ₁² >...

Question 7

A manufacturer of an automobile part has a process that is designed to produce the part with a target of 2.5 inches in length.In the past,the standard deviation of the length has been 0.035 inches.In an effort to reduce the variation in the process,the manufacturer has redesigned the process.A sample of 25 parts produced under the new process shows a sample standard deviation of 0.025 inches.Calculate the test statistic for testing whether the new process standard deviation has improved from the current process.

Accepted Answer

The answer of A manufacturer of an automobile part has...

Question 8

In a sample of n = 16 selected from a normally distributed population,we find a population standard deviation of s = 10.What is the value of χ² if we are testing H₀: σ² = 144?

Accepted Answer

The answer of In a sample of n = 16...

Question 9

A baker must monitor the temperature at which cookies are baked.Too much variation will cause inconsistency in the texture of the cookies.Past records show that the variance of the temperatures has been 1.44°.A random sample of 30 batches of cookies is selected,and the sample variance of the temperature is 4.41°.What is the 95 percent confidence interval for σ² at α = .05?

Accepted Answer

The answer of A baker must monitor the temperature at...

Question 10

Consider an engine parts supplier,and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are,respectively,2.5 inches and .00075.To reduce this variance,a new machine is designed.A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches,a variance of s² = .0002 (normal distribution).In order for a cylindrical engine part to give an engine long life,the outside diameter must be between 2.43 and 2.57 inches.Using the upper end of the 95 percent confidence interval for σ and assuming that μ = 2.5,determine whether 99.73 percent of the outside diameters produced by the new machine are within the specification limits.

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Question 11

What is the value of the computed F statistic for testing equality of population variances where s₁² = .004 and s₂² = .002? Consider H_A: σ₁² > σ₂²

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The answer of What is the value of the computed...

Question 12

When testing H₀: σ₁² = σ₁²,H_A: σ₁² > σ₂² at α = .01,where n₁ = 5,n₂ = 6,s₁² = 15,750,and s₂² = 10,920,what critical value do we use?

Accepted Answer

The answer of When testing H₀: σ₁² = σ₁²,H_A: σ₁²...

Question 13

When testing H₀: σ₁² ≤ σ₂² and H_A: σ₁² > σ₂²,where s₁² = .004,s₂² = .002,n₁ = 4,and n₂ = 7 at α = .05,what is the decision on H₀?

Accepted Answer

The answer of When testing H₀: σ₁² ≤ σ₂² and...

Question 14

When testing H₀: σ₁² ≤ σ₂² and H_A: σ₁² > σ₂²,where s₁² = .004,s₂² = .002,n₁ = 4,and n₂ = 7 at α = .05,what critical value do we use?

Accepted Answer

The answer of When testing H₀: σ₁² ≤ σ₂² and...

Question 15

Consider an engine parts supplier,and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are,respectively,2.5 inches and .00075.To reduce this variance,a new machine is designed.A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s² = .0002 (normal distribution).In order for a cylindrical engine part to give an engine long life,the outside diameter must be between 2.43 and 2.57 inches.Assuming normality,determine whether 99.73 percent of the outside diameters produced by the current machine are within specification limits.

Accepted Answer

The answer of Consider an engine parts supplier,and suppose the...

Question 16

A baker must monitor the temperature at which cookies are baked.Too much variation will cause inconsistency in the texture of the cookies.Past records show that the variance of the temperatures has been 1.44°.A random sample of 30 batches of cookies is selected,and the sample variance of the temperature is 4.41°.What is the test statistic for testing the null hypothesis that the population variance has increased above 1.44°?

Accepted Answer

The answer of A baker must monitor the temperature at...

Question 17

Consider an engine parts supplier,and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are,respectively,2.5 inches and .00075.To reduce this variance,a new machine is designed.A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches,a variance of s² = .0002 (normal distribution).In order for a cylindrical engine part to give an engine long life,the outside diameter must be between 2.43 and 2.57 inches.Find the 95 percent confidence intervals for σ² and σ.

Accepted Answer

The answer of Consider an engine parts supplier,and suppose the...

Question 18

Consider an engine parts supplier,and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are,respectively,2.5 inches and .00075.To reduce this variance,a new machine is designed.A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s² = .0002 (normal distribution).In order for a cylindrical engine part to give an engine long life,the outside diameter must be between 2.43 and 2.57 inches.If σ² denotes the variance of the population of all outside diameters that would be produced by the new machine,test H₀: σ² = .00075 versus H_a: σ² < .00075 by setting α = .05.

Accepted Answer

The answer of Consider an engine parts supplier,and suppose the...

Question 19

What is the value of the F statistic for H₀: σ₁² ≤ σ₁²,H_A: σ₁² > σ₁²,where s₁ = 3.3 and s₂ = 2.1?

Accepted Answer

The answer of What is the value of the F...

Question 20

A baker must monitor the temperature at which cookies are baked.Too much variation will cause inconsistency in the texture of the cookies.Past records show that the variance of the temperatures has been 1.44°.A random sample of 30 batches of cookies is selected,and the sample variance of the temperature is 4.41°.Test the hypothesis that the temperature variance has increased above 1.44° at α = .05.

Accepted Answer

The answer of A baker must monitor the temperature at...

Quiz 11: Statistical Inferences for Population Variances

In a sample of n = 25 selected from a normally distributed population,we find a population variance of s2 = 150.What is the value of χ2 if we are testing H0: σ2 = 100?

In a sample of n = 16 selected from a normally distributed population,we find a population standard deviation of s = 10.What are the degrees of freedom for the hypothesis test?

Two independent samples selected from two normally distributed populations have variances of σ12 and σ22 with n1 = 10 and n2 = 15.The degrees of freedom for the F distribution when testing the equality of the two population variances are:

Testing H0: σ12 = σ12,HA: σ12 > σ22 at α = .01,where n1 = 5,n2 = 6,s12 = 15,750,and s22 = 10,920,can we reject the null hypothesis?

In a sample of n = 16 selected from a normally distributed population,we find a population standard deviation of s = 10.What is the value of χ2 if we are testing H0: σ2 = 144?

What is the value of the computed F statistic for testing equality of population variances where s12 = .004 and s22 = .002? Consider HA: σ12 > σ22

When testing H0: σ12 = σ12,HA: σ12 > σ22 at α = .01,where n1 = 5,n2 = 6,s12 = 15,750,and s22 = 10,920,what critical value do we use?

When testing H0: σ12 ≤ σ22 and HA: σ12 > σ22,where s12 = .004,s22 = .002,n1 = 4,and n2 = 7 at α = .05,what is the decision on H0?

When testing H0: σ12 ≤ σ22 and HA: σ12 > σ22,where s12 = .004,s22 = .002,n1 = 4,and n2 = 7 at α = .05,what critical value do we use?

What is the value of the F statistic for H0: σ12 ≤ σ12,HA: σ12 > σ12,where s1 = 3.3 and s2 = 2.1?

In a sample of n = 25 selected from a normally distributed population,we find a population variance of s² = 150.What is the value of χ² if we are testing H₀: σ² = 100?

Two independent samples selected from two normally distributed populations have variances of σ₁² and σ₂² with n₁ = 10 and n₂ = 15.The degrees of freedom for the F distribution when testing the equality of the two population variances are:

Testing H₀: σ₁² = σ₁²,H_A: σ₁² > σ₂² at α = .01,where n₁ = 5,n₂ = 6,s₁² = 15,750,and s₂² = 10,920,can we reject the null hypothesis?

In a sample of n = 16 selected from a normally distributed population,we find a population standard deviation of s = 10.What is the value of χ² if we are testing H₀: σ² = 144?

What is the value of the computed F statistic for testing equality of population variances where s₁² = .004 and s₂² = .002? Consider H_A: σ₁² > σ₂²

When testing H₀: σ₁² = σ₁²,H_A: σ₁² > σ₂² at α = .01,where n₁ = 5,n₂ = 6,s₁² = 15,750,and s₂² = 10,920,what critical value do we use?

When testing H₀: σ₁² ≤ σ₂² and H_A: σ₁² > σ₂²,where s₁² = .004,s₂² = .002,n₁ = 4,and n₂ = 7 at α = .05,what is the decision on H₀?

When testing H₀: σ₁² ≤ σ₂² and H_A: σ₁² > σ₂²,where s₁² = .004,s₂² = .002,n₁ = 4,and n₂ = 7 at α = .05,what critical value do we use?

What is the value of the F statistic for H₀: σ₁² ≤ σ₁²,H_A: σ₁² > σ₁²,where s₁ = 3.3 and s₂ = 2.1?