Statistics- STA2023 Extra Credit #3 (chapters 15-19)

QUESTION

STA2023Extra Credit #3 (chapters 15-19)Directions:Answer the questions on this pdf. Then use your answers to complete the “quiz” located in theExtra Credit #3 Assignment on Canvas.I will post worked out solutions after the due dateNote:I will not necessarily ask you all of these questions on Test 3, but this is an excellent study guidefor Test 3. However, on Test 3, I will not guide you as I did below with what conditions you aresupposed to check (ie the green areas will not be on your test). I will expect you to know whichconditions you are supposed to check.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 lessthan 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 deviation20 hours.a. What is the probability that a randomly selected light bulb will last more that 210 hours?Probability:b. 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 inghosts?a. What is the population of interest?Population:b. Describe p in words.p:c. Write the Hypotheses.H0:HA:d. Perform the test using a significance level of 0.10 ( = 0.10)Be sure to show the following:i. Check Assumptions and Conditionsii. Find the P-value.iii. Give the conclusion in context. (3 things needed)i. Conditions:Randomization:10% Condition:Success/Failure Condition:ii. P-value:iii. Conclusion in context:e. Explain what the P-value you found means in the context of the problemExplanation:f.What would be a Type I Error in the context of this problem?Type I Error:g. What would be a Type II Error in the context of this problem?Type II Error:h. Check the assumptions and conditions necessary for finding a confidence interval for p.Conditions:Randomization:10% Condition:Success/Failure Condition:i.Find a 95% confidence interval for p.Interval:j.Give your interval in context of the problem.Interval in Context:k. Interpret what 95% confidence means in this context.Interpretation:l.What sample size would allow us to increase our confidence level to 99% while reducing the margin oferror 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 thatgroup, the mean weight was 2910 pounds with a standard deviation of 532 pounds. Is this strong evidence that themean weight of all cars is not 3000 pounds?a. What is the population of interest?Population:b. Describein words.:c. Write the HypothesesH0:HA:d. Perform the test using a significance level of 0.05 ( = 0.05)Be sure to show the following:i. Check Assumptions and Conditionsii. Find the P-value.iii. Give the conclusion in context. (3 things needed)i. Conditions:Randomization:10% Condition:Nearly Normal:ii. P-value:iii. Conclusion in context:e. Explain what the P-value you found means in the context of the problemExplanation:f.What would be a Type I Error in the context of this problem?Type I Error:g. What would be a Type II Error in the context of this problem?Type II Error:h. Find a 90% confidence interval for.Interval:i.Give your interval in context of the problem.Interval in Context:j.Interpret what 90% confidence means in this context.Interpretation:k. What sample size would allow us to increase our confidence level to 95% while reducing the margin oferror to only 50 pounds?Sample size:

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