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STA2023 Extra Credit #3 (chapters 15-19)

Directions: Answer the questions on this pdf. Then use your answers to complete the “quiz” located in the

Extra Credit #3 Assignment on Canvas.

I will post worked out solutions after the due date 

Note: I will not necessarily ask you all of these questions on Test 3, but this is an excellent study guide

for Test 3. However, on Test 3, I will not guide you as I did below with what conditions you are

supposed to check (ie the green areas will not be on your test). I will expect you to know which

conditions 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 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.

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 in

ghosts?

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 Conditions ii. 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 problem

Explanation:

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 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?

a. What is the population of interest?

Population:

b. Describe  in words.

:

c. Write the Hypotheses

H0:

HA:

d. Perform the test using a significance level of 0.05 ( = 0.05) Be sure to show the following:

i. Check Assumptions and Conditions ii. 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 problem

Explanation:

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 of error to only 50 pounds?

Sample size: