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

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: