Stats Extra Credit 3


    

Round all your answers to 4 decimal places. Part I (Focusing on Chapter 15) 

  1. Suppose 14% of people are left handed. What is the probability that a random sample of 200 people will have less than 12% lefties? Be sure to check the conditions to make the necessary assumptions before using the model.
    Conditions: Randomization: 10% Condition:
    Success/Failure Condition:
    Probability:
     
  2. The life of General Electric light bulbs are normally distributed with a mean of 200 hours and a standard deviation 20 hours.
     

    1. What is the probability that a randomly selected light bulb will last more that 210 hours?
      Probability:
       
    2. What is the probability that a random sample of 10 light bulbs has a mean life greater than 210 hours? (check assumptions and conditions first)
      Conditions: Randomization: 10% Condition:
      Large Enough Sample Condition:
       

 

Probability: 

  

Part II (Focusing on Chapters 16-17 and 19) 

 

3. In 2005, the Gallup Poll estimated that 32% of adults believe in ghosts. In a random sample of 200 young adults (ages 18-29), 38% said they believed in ghosts. Is this evidence that young adults are more likely to believe in ghosts? 

  1. What is the population of interest?
    Population:
     
  2. Describe p in words. p:
     
  3. Write the Hypotheses.
    H0:
    HA:
     
  4. Perform the test using a significance level of 0.10 ( = 0.10)
     

 

Be sure i. 

ii. iii. 

i. 

ii. 

iii. 

to show the following:
Check Assumptions and Conditions
Find the P-value.
Give the conclusion in context. (3 things needed) 

Conditions: Randomization: 10% Condition: 

Success/Failure Condition: 

P-value: 

Conclusion in context: 

  

  1. Explain what the P-value you found means in the context of the problem
    Explanation:
     
  2. What would be a Type I Error in the context of this problem?
    Type I Error:
     
  3. What would be a Type II Error in the context of this problem?
     

 

Type II Error: 

   

  1. Check the assumptions and conditions necessary for finding a confidence interval for p. Conditions: Randomization:
    10% Condition: Success/Failure Condition:
     
  2. Find a 95% confidence interval for p. Interval:
     
  3. Give your interval in context of the problem.
    Interval in Context:
     
  4. Interpret what 95% confidence means in this context.
    Interpretation:
     
  5. What sample size would allow us to increase our confidence level to 99% while reducing the margin of error to only 0.03?
    Sample size:
     

  

Part III (Focusing on Chapter 18-19) 

4. Insurance companies are interested in knowing the mean weight of cars currently licensed in the United States; they believe it is 3000 pounds. To see if the estimate is correct, they check a random sample of 80 cars. For that group, the mean weight was 2910 pounds with a standard deviation of 532 pounds. Is this strong evidence that the mean weight of all cars is not 3000 pounds? 

  1. What is the population of interest?
    Population:
     
  2. Describe  in words. :
     
  3. Write the Hypotheses
    H0:
    HA:
     
  4. Perform the test using a significance level of 0.05 ( = 0.05)
     

 

Be sure i. 

ii. iii. 

i. 

ii. 

iii. 

to show the following:
Check Assumptions and Conditions
Find the P-value.
Give the conclusion in context. (3 things needed) 

Conditions: Randomization: 10% Condition: Nearly Normal: 

P-value: 

Conclusion in context: 

  

  1. Explain what the P-value you found means in the context of the problem
    Explanation:
     
  2. What would be a Type I Error in the context of this problem?
    Type I Error:
     
  3. What would be a Type II Error in the context of this problem?
     

 

Type II Error: 

   

  1. Find a 90% confidence interval for  . Interval:
     
  2. Give your interval in context of the problem.
    Interval in Context:
     
  3. Interpret what 90% confidence means in this context.
    Interpretation:
     
  4. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 50 pounds?
    Sample size:
     
Stats Extra Credit 3


    

Round all your answers to 4 decimal places. Part I (Focusing on Chapter 15) 

  1. Suppose 14% of people are left handed. What is the probability that a random sample of 200 people will have less than 12% lefties? Be sure to check the conditions to make the necessary assumptions before using the model.
    Conditions: Randomization: 10% Condition:
    Success/Failure Condition:
    Probability:
     
  2. The life of General Electric light bulbs are normally distributed with a mean of 200 hours and a standard deviation 20 hours.
     

    1. What is the probability that a randomly selected light bulb will last more that 210 hours?
      Probability:
       
    2. What is the probability that a random sample of 10 light bulbs has a mean life greater than 210 hours? (check assumptions and conditions first)
      Conditions: Randomization: 10% Condition:
      Large Enough Sample Condition:
       

 

Probability: 

  

Part II (Focusing on Chapters 16-17 and 19) 

 

3. In 2005, the Gallup Poll estimated that 32% of adults believe in ghosts. In a random sample of 200 young adults (ages 18-29), 38% said they believed in ghosts. Is this evidence that young adults are more likely to believe in ghosts? 

  1. What is the population of interest?
    Population:
     
  2. Describe p in words. p:
     
  3. Write the Hypotheses.
    H0:
    HA:
     
  4. Perform the test using a significance level of 0.10 ( = 0.10)
     

 

Be sure i. 

ii. iii. 

i. 

ii. 

iii. 

to show the following:
Check Assumptions and Conditions
Find the P-value.
Give the conclusion in context. (3 things needed) 

Conditions: Randomization: 10% Condition: 

Success/Failure Condition: 

P-value: 

Conclusion in context: 

  

  1. Explain what the P-value you found means in the context of the problem
    Explanation:
     
  2. What would be a Type I Error in the context of this problem?
    Type I Error:
     
  3. What would be a Type II Error in the context of this problem?
     

 

Type II Error: 

   

  1. Check the assumptions and conditions necessary for finding a confidence interval for p. Conditions: Randomization:
    10% Condition: Success/Failure Condition:
     
  2. Find a 95% confidence interval for p. Interval:
     
  3. Give your interval in context of the problem.
    Interval in Context:
     
  4. Interpret what 95% confidence means in this context.
    Interpretation:
     
  5. What sample size would allow us to increase our confidence level to 99% while reducing the margin of error to only 0.03?
    Sample size:
     

  

Part III (Focusing on Chapter 18-19) 

4. Insurance companies are interested in knowing the mean weight of cars currently licensed in the United States; they believe it is 3000 pounds. To see if the estimate is correct, they check a random sample of 80 cars. For that group, the mean weight was 2910 pounds with a standard deviation of 532 pounds. Is this strong evidence that the mean weight of all cars is not 3000 pounds? 

  1. What is the population of interest?
    Population:
     
  2. Describe  in words. :
     
  3. Write the Hypotheses
    H0:
    HA:
     
  4. Perform the test using a significance level of 0.05 ( = 0.05)
     

 

Be sure i. 

ii. iii. 

i. 

ii. 

iii. 

to show the following:
Check Assumptions and Conditions
Find the P-value.
Give the conclusion in context. (3 things needed) 

Conditions: Randomization: 10% Condition: Nearly Normal: 

P-value: 

Conclusion in context: 

  

  1. Explain what the P-value you found means in the context of the problem
    Explanation:
     
  2. What would be a Type I Error in the context of this problem?
    Type I Error:
     
  3. What would be a Type II Error in the context of this problem?
     

 

Type II Error: 

   

  1. Find a 90% confidence interval for  . Interval:
     
  2. Give your interval in context of the problem.
    Interval in Context:
     
  3. Interpret what 90% confidence means in this context.
    Interpretation:
     
  4. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 50 pounds?
    Sample size:
     

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