A sample of birth weights of 35 girls was taken. Below are the results (in g):   2991.9 3538.6 3780.4 2622.2 3601.7 3833.8 3497.5 3665.8 3702.2 3771.9 3308.9 3428.5 2857.1 3422.9 3218.2 3052.4 3320.1 3380.3 2989.5 3642 3383.3 4131.4 3194.3 3298.4 4536.2 3290.4 3479.9 4385.3 3828.1 3165.7 2976.7 2877.2 4162.4 3239.9 2957   (Note: The average and the standard deviation of the data are respectively 3443.8 g and 435.92 g.) Use a 5% significance level to test the claim that the standard deviation of birthweights of girls is less than the standard deviation of birthweights of boys, which is 500 g. Procedure: Select an answer One mean T Hypothesis Test One proportion Z Hypothesis Test One variance χ² Hypothesis Test One mean Z Hypothesis Test  Assumptions: (select everything that applies) Sample size is greater than 30 Population standard deviation is unknown The number of positive and negative responses are both greater than 10 Population standard deviation is known Simple random sample Normal population   Step 1. Hypotheses Set-Up: H0:H0: Select an answer p μ σ²  = , where ? σ p μ  is the Select an answer population proportion population standard deviation population mean  and the units are ? mg g lbs kg   Ha:Ha: Select an answer σ² p μ  ? > < ≠   , and the test is Select an answer Two-Tailed Left-Tailed Right-Tailed  Step 2. The significance level α=α= % Step 3. Compute the value of the test statistic: Select an answer χ₀² t₀ z₀  = (Round the answer to 3 decimal places) Step 4. Testing Procedure: (Round the answers to 3 decimal places) CVA PVA Provide the critical value(s) for the Rejection Region: Compute the P-value of the test statistic: left CV is  and right CV is  P-value is  Step 5. Decision: CVA PVA Is the test statistic in the rejection region? Is the P-value less than the significance level? ? no yes  ? yes no  Conclusion: Select an answer Reject the null hypothesis in favor of the alternative. Do not reject the null hypothesis in favor of the alternative.  Step 6. Interpretation: At 5% significance level we Select an answer DO DO NOT  have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter29: Tolerance, Clearance, And Interference
Section: Chapter Questions
Problem 16A: Spacers are manufactured to the mean dimension and tolerance shown in Figure 29-12. An inspector...
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A sample of birth weights of 35 girls was taken. Below are the results (in g):

 

2991.9 3538.6 3780.4 2622.2 3601.7
3833.8 3497.5 3665.8 3702.2 3771.9
3308.9 3428.5 2857.1 3422.9 3218.2
3052.4 3320.1 3380.3 2989.5 3642
3383.3 4131.4 3194.3 3298.4 4536.2
3290.4 3479.9 4385.3 3828.1 3165.7
2976.7 2877.2 4162.4 3239.9 2957

 

(Note: The average and the standard deviation of the data are respectively 3443.8 g and 435.92 g.)

Use a 5% significance level to test the claim that the standard deviation of birthweights of girls is less than the standard deviation of birthweights of boys, which is 500 g.

Procedure: Select an answer One mean T Hypothesis Test One proportion Z Hypothesis Test One variance χ² Hypothesis Test One mean Z Hypothesis Test 

Assumptions: (select everything that applies)

  • Sample size is greater than 30
  • Population standard deviation is unknown
  • The number of positive and negative responses are both greater than 10
  • Population standard deviation is known
  • Simple random sample
  • Normal population

 

Step 1. Hypotheses Set-Up:

H0:H0: Select an answer p μ σ²  = , where ? σ p μ  is the Select an answer population proportion population standard deviation population mean  and the units are ? mg g lbs kg 
 Ha:Ha: Select an answer σ² p μ  ? > < ≠   , and the test is Select an answer Two-Tailed Left-Tailed Right-Tailed 

Step 2. The significance level α=α= %

Step 3. Compute the value of the test statistic: Select an answer χ₀² t₀ z₀  = (Round the answer to 3 decimal places)

Step 4. Testing Procedure: (Round the answers to 3 decimal places)

CVA PVA
Provide the critical value(s) for the Rejection Region: Compute the P-value of the test statistic:
left CV is  and right CV is  P-value is 

Step 5. Decision:

CVA PVA
Is the test statistic in the rejection region? Is the P-value less than the significance level?
? no yes  ? yes no 

Conclusion: Select an answer Reject the null hypothesis in favor of the alternative. Do not reject the null hypothesis in favor of the alternative. 

Step 6. Interpretation:

At 5% significance level we Select an answer DO DO NOT  have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

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ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,