Question 1

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

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Question 2

A fast food company uses two management-training methods.Method 1 is a traditional method of training and Method 2 is a new and innovative method.The company has just hired 36 new management trainees.15 of the trainees are randomly selected and assigned to the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method.Assume equal population variances and normally distributed populations. $$\begin{array} { l c c } 
& \text { Mean } & \text { Standard deviation } \
\text { Method 1 } & 69 & 3.4 \
\text { Method 2 } & 72 & 3.8
\end{array}$$
-Write the alternative hypothesis.

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Question 3

The accompanying data are the times in seconds that it took a sample of employees to assemble a component at Ental Industries manufacturing facility.Assembly times are normally distributed.At the .05 significance level,can we conclude that the mean assembly time for this component is not equal to 3 minutes? Use H_A: μ ≠ 180.

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Question 4

A fast food company uses two management-training methods.Method 1 is a traditional method of training and Method 2 is a new and innovative method.The company has just hired 36 new management trainees.15 of the trainees are randomly selected and assigned to the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method.Assume equal population variances and normally distributed populations. $$\begin{array} { l c c } 
& \text { Mean } & \text { Standard deviation } \
\text { Method 1 } & 69 & 3.4 \
\text { Method 2 } & 72 & 3.8
\end{array}$$
-What is the critical value for this test at alpha = .01?

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Question 5

Two parameters of the F distribution are:

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Question 6

What is the F-statistic for testing H₀: σ₁² ≤σ₂²,H_A: σ₂² > σ₁² at σ = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

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Question 7

A fast food company uses two management-training methods.Method 1 is a traditional method of training and Method 2 is a new and innovative method.The company has just hired 36 new management trainees.15 of the trainees are randomly selected and assigned to the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method.Assume equal population variances and normally distributed populations. $$\begin{array} { l c c } 
& \text { Mean } & \text { Standard deviation } \
\text { Method 1 } & 69 & 3.4 \
\text { Method 2 } & 72 & 3.8
\end{array}$$
-Write the null hypothesis.

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Question 8

A fast food company uses two management-training methods.Method 1 is a traditional method of training and Method 2 is a new and innovative method.The company has just hired 36 new management trainees.15 of the trainees are randomly selected and assigned to the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method.Assume equal population variances and normally distributed populations. $$\begin{array} { l c c } 
& \text { Mean } & \text { Standard deviation } \
\text { Method 1 } & 69 & 3.4 \
\text { Method 2 } & 72 & 3.8
\end{array}$$
-What is the sample value of the test statistic?

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Question 9

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

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Question 10

Calculate the pooled variance where sample 1 has data: 16,14,19,18,19,20,15,18,17,18,and sample 2 has data: 13,19,14,17,21,14,15,10,13,15.

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Question 11

Calculate the t statistic for testing equality of means where $\bar { X }$ ₁ = 8.2, $\bar { X }$ ₂ = 11.3,s₁² = 5.4,s₂² = 5.2,n₁ = 6,n₂ = 7.Assume equal population variances. t = -2.63

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Question 12

Test H₀: σ₁² ≤σ₂² H_A: σ₁² > σ₂² where s₁² = .004,s₂² = .002,n₁ = 4,n₂ = 7 at α = .05.

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Question 13

Use the following data and test the equality of variances for two populations at ? = .10,where sample 1 is randomly selected from population 1 and sample 2 is randomly selected from population 2.Assume normally distributed populations.

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Question 14

Test the equality of means at  $\alpha$ 
= .05,where sample 1 has data:16,14,19,18,19,20,15,18,17,18,and sample 2 has data:13,19,14,17,21,14,15,10,13,15.Assume equal population variances,normally distributed populations,and independent random samples.

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Question 15

A fast food company uses two management-training methods.Method 1 is a traditional method of training and Method 2 is a new and innovative method.The company has just hired 36 new management trainees.15 of the trainees are randomly selected and assigned to the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method.Assume equal population variances and normally distributed populations. $$\begin{array} { l c c } 
& \text { Mean } & \text { Standard deviation } \
\text { Method 1 } & 69 & 3.4 \
\text { Method 2 } & 72 & 3.8
\end{array}$$
-What is the critical value for this test at alpha = .05?

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Question 16

Test H₀: σ₁² ≤σ₂²,H_A: σ₁² > σ₂² at alpha = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

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Question 17

Test H₀: σ₁² = σ₁²,H_A: σ₁² > σ₂² at alpha = .01 where n₁ = 5,n₂ = 6,s₁² = 15750,s₂² = 10920.Assume normally distributed populations and independent random samples.

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Question 18

A fast food company uses two management-training methods.Method 1 is a traditional method of training and Method 2 is a new and innovative method.The company has just hired 36 new management trainees.15 of the trainees are randomly selected and assigned to the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method.Assume equal population variances and normally distributed populations. $$\begin{array} { l c c } 
& \text { Mean } & \text { Standard deviation } \
\text { Method 1 } & 69 & 3.4 \
\text { Method 2 } & 72 & 3.8
\end{array}$$
-Is there sufficient evidence to conclude that the new training method is more effective than the traditional training method? What is the decision at alpha = .05?

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Question 19

Test HS1U1B10S1U1B0: $\mu$S1U1B11S1U1B0 $\le$ $\mu$S1U1B12S1U1B0 ,HS1U1B1AS1U1B0: $\mu$S1U1B11S1U1B0 > $\mu$S1U1B12S1U1B0 at $\alpha$ = .10,where $$\bar { X } _ { 1 }$$= 77.4, 
$$\bar { X } _ { 2 }$$= 72.2,sS1U1B11S1U1B0 = 3.3,sS1U1B12S1U1B0 = 2.1,nS1U1B11S1U1B0 = 6,nS1U1B12S1U1B0 = 6.Assume equal population variances,normally distributed populations,and independent random samples.
Reject HS1U1B10S1U1B0S1U1B1

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Question 20

In testing the equality of population variance,what two assumptions are required?

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Quiz 8: Hypothesis Testing

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

Two parameters of the F distribution are:

What is the F-statistic for testing H₀: σ₁² ≤σ₂²,H_A: σ₂² > σ₁² at σ = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

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

Calculate the pooled variance where sample 1 has data: 16,14,19,18,19,20,15,18,17,18,and sample 2 has data: 13,19,14,17,21,14,15,10,13,15.

Calculate the t statistic for testing equality of means where $\bar { X }$ ₁ = 8.2, $\bar { X }$ ₂ = 11.3,s₁² = 5.4,s₂² = 5.2,n₁ = 6,n₂ = 7.Assume equal population variances. t = -2.63

Test H₀: σ₁² ≤σ₂² H_A: σ₁² > σ₂² where s₁² = .004,s₂² = .002,n₁ = 4,n₂ = 7 at α = .05.

Use the following data and test the equality of variances for two populations at ? = .10,where sample 1 is randomly selected from population 1 and sample 2 is randomly selected from population 2.Assume normally distributed populations.

Test the equality of means at $\alpha$ = .05,where sample 1 has data:16,14,19,18,19,20,15,18,17,18,and sample 2 has data:13,19,14,17,21,14,15,10,13,15.Assume equal population variances,normally distributed populations,and independent random samples.

Test H₀: σ₁² ≤σ₂²,H_A: σ₁² > σ₂² at alpha = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

Test H₀: σ₁² = σ₁²,H_A: σ₁² > σ₂² at alpha = .01 where n₁ = 5,n₂ = 6,s₁² = 15750,s₂² = 10920.Assume normally distributed populations and independent random samples.

Test H₀: $\mu$ ₁ $\le$ $\mu$ ₂ ,H_A: $\mu$ ₁ > $\mu$ ₂ at $\alpha$ = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6.Assume equal population variances,normally distributed populations,and independent random samples. Reject H₀

In testing the equality of population variance,what two assumptions are required?

Quiz 8: Hypothesis Testing

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

Two parameters of the F distribution are:

What is the F-statistic for testing H0: σ12 ≤σ22,HA: σ22 > σ12 at σ = .05 where n1 = 16,n2 = 19,s12 = .03,s22 = .02.

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

Calculate the pooled variance where sample 1 has data: 16,14,19,18,19,20,15,18,17,18,and sample 2 has data: 13,19,14,17,21,14,15,10,13,15.

Calculate the t statistic for testing equality of means where Xˉ\bar { X }Xˉ 1 = 8.2, Xˉ\bar { X }Xˉ 2 = 11.3,s12 = 5.4,s22 = 5.2,n1 = 6,n2 = 7.Assume equal population variances. t = -2.63

Test H0: σ12 ≤σ22 HA: σ12 > σ22 where s12 = .004,s22 = .002,n1 = 4,n2 = 7 at α = .05.

Use the following data and test the equality of variances for two populations at ? = .10,where sample 1 is randomly selected from population 1 and sample 2 is randomly selected from population 2.Assume normally distributed populations.

Test the equality of means at α\alphaα = .05,where sample 1 has data:16,14,19,18,19,20,15,18,17,18,and sample 2 has data:13,19,14,17,21,14,15,10,13,15.Assume equal population variances,normally distributed populations,and independent random samples.

Test H0: σ12 ≤σ22,HA: σ12 > σ22 at alpha = .05 where n1 = 16,n2 = 19,s12 = .03,s22 = .02.

Test H0: σ12 = σ12,HA: σ12 > σ22 at alpha = .01 where n1 = 5,n2 = 6,s12 = 15750,s22 = 10920.Assume normally distributed populations and independent random samples.

In testing the equality of population variance,what two assumptions are required?

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

What is the F-statistic for testing H₀: σ₁² ≤σ₂²,H_A: σ₂² > σ₁² at σ = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

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

Calculate the t statistic for testing equality of means where $\bar { X }$ ₁ = 8.2, $\bar { X }$ ₂ = 11.3,s₁² = 5.4,s₂² = 5.2,n₁ = 6,n₂ = 7.Assume equal population variances. t = -2.63

Test H₀: σ₁² ≤σ₂² H_A: σ₁² > σ₂² where s₁² = .004,s₂² = .002,n₁ = 4,n₂ = 7 at α = .05.

Test the equality of means at $\alpha$ = .05,where sample 1 has data:16,14,19,18,19,20,15,18,17,18,and sample 2 has data:13,19,14,17,21,14,15,10,13,15.Assume equal population variances,normally distributed populations,and independent random samples.

Test H₀: σ₁² ≤σ₂²,H_A: σ₁² > σ₂² at alpha = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

Test H₀: σ₁² = σ₁²,H_A: σ₁² > σ₂² at alpha = .01 where n₁ = 5,n₂ = 6,s₁² = 15750,s₂² = 10920.Assume normally distributed populations and independent random samples.