# 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: