Stats 250 W16 HW 3 complete solutions correct answers key

Stats 250 W16 HW 3 complete solutions correct answers key

Question 1 Background :
Bachelor's Degree Education Rate
Education Rate - According to the Department of Education, 32% of adults over the age of 25 in the
United States have earned at least a bachelor’s degree. Suppose this is the true proportion of all adults
over the age of 25 that have earned at least a bachelor’s degree. A random sample of 200 adults over the
age of 25 will be selected and their highest degree will be recorded. Let pp̂ represent the proportion of
adults over the age of 25 in the sample who have earned at least a bachelor’s degree.

Question 1 Subquestions
1.a
1 point(s)
Consider all the possible values for the resulting sample proportion pp̂. What is the expected value (or
average) of all such values of pp̂?
•
•
32
64
0.32
unknown since we have not yet taken an actual random sample yet

1.b
1 point(s)
Consider all the possible values for the resulting sample proportion pp̂. What is the standard deviation of
all such values of pp̂?
•
•0.001088
0.03298
6.596969
unknown since we have not yet taken an actual random sample yet

1.c
1 point(s)
Perform the check regarding the sample size that confirms the sampling distribution of the possible values
for pp̂ will be approximately normally distributed.
Student answer
No answer entered.
Question 2 Background :
Facebook: Top Source for News
A poll based on a random sample of 1,820 American adults (aged 18 and older, living in all 50 U.S. states
and the District of Columbia) was conducted to study the source of news for Americans. The study
reports that the proportion of all Americans who use Facebook as their source of news is estimated to be
61%.

Question 2 Subquestions
2.a
2 point(s)
Give a 99% conservative confidence interval for the proportion of all such Americans who would say
Facebook is their source of news. Show all work.
Student answer
No answer entered.
2.b
1 point(s)
The study went on to report the results by age group. If the results were used to make a 99% conservative
confidence interval for the proportion of all Americans who are in their 30s (using only the subset of the
1820 Americans surveyed who are in their 30s), the corresponding margin of (sampling) error would have
been…
• smaller
• larger
2.c
1 point(s)
The study included the following statement in the footnote: “In addition to sampling error, question
wording in surveys can introduce error or bias into the findings of public opinion polls.” Name the type of
bias that the wording of the question could introduce.
• selection bias
• non-participation (non-response) bias
• response bias
2.d

2 point(s)
A researcher plans to conduct a similar study on Ann Arbor adult residents. Suppose the researcher would
like the sample size to be large enough so that they can be 90% confident in reporting the estimated
proportion within 3% of the population proportion. What is the minimum sample size the researcher
would need? As with any questions, you need to show your work.
Student answer
No answer entered.
Question 3 Background :
Estimating Proportion of Coffee Drinkers
In a recent survey of 150 students at a community college, 86 students said they were “regular” coffee
drinkers. Based on these results, the 95% confidence interval to estimate the population proportion of all
such college students who drink coffee regularly was found to be: 0.573 ± 0.079 or 0.494 to 0.652.

Question 3 Subquestions
3.a
1 point(s)
Which of the following correspond to the value of 0.573?
•
•the sample proportion
the population proportion
the margin of error
the confidence level

3.b
1 point(s)
Which of the following correspond to the value of 0.079?
•
•the sample proportion
the population proportion
the margin of error
the confidence level

3.c
1 point(s)
Based on this reported confidence interval, does there appear to be significant evidence (at a 95%
confidence level) to conclude there is a majority of regular coffee drinkers in the community college
population? Select the answer with the appropriate explanation.
• Yes, because 57.3% is above 50%.
• Yes, because 95% is above 50%.
• No, because the interval of reasonable values dips below 50%.
• No, because 0.079 is below 50%.
Question 4 Background :
In-State University?
Based on a random sample of 1,250 college students, a 95% confidence interval for the population
proportion of all college students who attend an in-state university was reported as 66% to 72%.
Determine whether each of the following statements is an appropriate statement that could be included in
the report summarizing these results.

Question 4 Subquestions
4.a
1 point(s)
With 95% confidence we estimate the population proportion of all college students who attend an in-state
university is between 0.66 and 0.72.
• Appropriate
• Not Appropriate
4.b
1 point(s)
There is a 95% chance that the population proportion of all college students who attend an in-state
university is between 0.66 and 0.72.
• Appropriate
• Not appropriate
4.c
1 point(s)
If this survey were replicated many times, each replication providing a 95% confidence interval for the
population proportion of all college students who attend an in-state university, then 95% of the resulting
confidence intervals would be expected to capture the sample proportion of college students who attend
an in-state university.
• Appropriate
• Not appropriate
4.d
1 point(s)
We would estimate that 69% of all college students attend an in-state university with a 95% margin of
error of 3%.
• Appropriate

• Not appropriate
1 point(s)
Question 5 :
Who needs more?
Estimating a Population Proportion. Suppose two researchers want to make a conservative confidence
interval to estimate the proportion of American college students who favor abolishing the penny. They
both want to have about the same margin of error to estimate this proportion. However, Researcher 1
wants to estimate with 99% confidence and Researcher 2 wants to estimate with 95% confidence. Which
researcher would need more students for their study in order to obtain the desired margin of error? Select
your answer from the following options.

Question 5 Multiple Choice Options
•
•
•
•

Researcher 1.
Researcher 2.
Both researchers would need the same number of subjects.
It is impossible to obtain the same margin of error with the two different confidence levels.

Question 6 Background :
Plastic or Paper?
Consider the following quote: “In a recent survey, 61% of the sampled consumers said they prefer
recyclable plastic grocery bags (rather than paper). If there were no preference (that is, if the true
proportion of all consumers who prefer recyclable plastic (over paper) bags is 0.50), the chance of
observing the result of 61% or something even larger would be only about 0.03. Because 0.03 is less than
0.05, we can conclude a statistically significant preference for recyclable plastic bags.”

Question 6 Subquestions
6.a
1 point(s)
For this study, the p-value of the test is:
• 0.03
• 0.05
• 0.61
6.b
1 point(s)
For this study, the significance level of the test is:
• 0.03

• 0.05
• 0.61
6.c
1 point(s)
Which of the following phrases is appropriate for the value of 0.61? Select all that apply.
•
•
•
•

the sample proportion
the population proportion
a statistic
a parameter

6.d
1 point(s)
Which of the following represent the hypotheses being tested in this study?
•
H0: p = 0.61 versus Ha: p > 0.61
H0: p = 0.61 versus Ha: p < 0.61
H0: p = 0.50 versus Ha: p = 0.61
H0: p = 0.50 versus Ha: p > 0.50

1 point(s)
Question 7 :
Statistical Significance
Suppose the results of a hypothesis test are statistically significant at the 5% level. Which of the
following statements are true? (Mark all that are true.)

Question 7 Multiple Choice Options
•
•The results are definitely statistically significant at the 10% level.
The results are definitely statistically significant at the 1% level.
The p-value is greater than 0.05.
The p-value is less than or equal to 0.05.

Question 8 Background :
Super Bowl: A Fair Coin or not
Suppose your company had designed and created a memorial coin for the next Super Bowl. The “master”
coin would be used for the ceremonial coin-flip to begin the game and fans could order a replica of that
coin for themselves. It’s very important that the master coin be fair, that is, that the probability of heads of
the master coin be 0.50. The NFL requires a formal report as to the scientific assessment of that
probability.

Suppose it was decided that once the master coin was created, a study would be conducted where the coin
would be tossed on artificial turf 500 times and the number of heads would be recorded. The study plan is
to test H0: p = 0.50 versus Ha: p ≠ 0.50 at a 5% significance level.
Of these 500 tosses, 261 resulted in “heads” for a sample proportion of 0.522.

Question 8 Subquestions
8.a
2 point(s)
Assuming one can consider these tosses as random and independent, check the remaining condition that is
needed in order to conduct a large sample z test of the hypotheses. Show your work.
Student answer
No answer entered.
8.b
2 point(s)
Compute the observed z test statistic value. Show your work.
Student answer
No answer entered.
8.c
3 point(s)
Find the corresponding p-value for this test. Include a complete sketch or graph of the p-value as part of
your work, shading the p-value area and labeling the distribution and x axis.

Student answer
No answer entered.
8.d
1 point(s)
At a 10% significance level, the decision is to fail to reject the null hypothesis. Which of the following is
the appropriate conclusion?
• There is insufficient evidence to show the coin is biased, so the master coin could be used in the
ceremonial coin-flip.
• There is sufficient evidence to show the coin is biased, that is, the master coin should not be used
in the ceremonial coin-flip.
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