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Sophia Introduction to Statistics Final Milestone
(Below is a compilation of all questions for Final Milestone. The answers are 100% correct, and it
guaranteed to earn you a perfect score in this unit. For a faster search, just hit on ctrl f on windows, or
command f on mac. Good luck!)
You passed this Milestone
25 questions were answered correctly.
1
What is the probability of NOT rolling a four when rolling a six sided die?
•
•
•
•
RATIONALE
Recall that the probability of a complement, or the probability of something NOT
happening, can be calculated by finding the probability of that event happening, and
then subtracting from 1. Note that the probability of rolling a four would be 1/6. So
the probability of NOT rolling a four is equivalent to:
CONCEPT
Complement of an Event
2
Select the following statement that describes non-overlapping events.
• Jon needs to roll an even number to win. When it’s his turn, he rolls a two.
• To win, Jon needs a red card. He receives a Queen of Diamonds.
• Receiving the King of Hearts fulfills Jon's need of getting both a face card and a
heart.
• Jon wants a face card so he can have a winning hand, and he receives the eight of
clubs.
RATIONALE
Events are non-overlapping if the two events cannot both occur in a single trial of a
chance experiment. Since he wants a face card {Jack, Queen or King} and he got
an eight {8}, there is no overlap.
, CONCEPT
Overlapping Events
3
Rob sent an email survey to 2,000 cell phone owners asking about their satisfaction
with their current plan. Only 256 people returned the survey and they were
predominately 18-24 years old.
Which of the following statements is true?
• The survey suffers from census issues because only 256 people responded.
• Rob included too many people on the survey list, affecting the data collected.
• Rob is ignoring the assumption that all survey participants will want to act
independently.
• The survey likely has bias because the people who could not answer differ from
those who did answer.
RATIONALE
In this survey there was a very low response rate with only 256 of the 2000. The
characteristics of those who responded are different from non-responders. Since the
responders and non-responders differ, we would worry about this affecting how they
responded.
CONCEPT
Bias
4
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of
customers follows a uniform distribution, a chi-square test for goodness of fit should be
performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest
hundredth.
• 0.67
,• 0.40
• 2.33
• 1.60
RATIONALE
Using the chi-square formula we can note the test statistic is
CONCEPT
Chi-Square Test for Goodness-of-Fit
5
What value of z* should be used to construct a 98% confidence interval of a
population mean? Answer choices are rounded to the thousandths place.
, • 2.055
• 2.325
• 1.175
• 1.645
RATIONALE
Using the z-chart to construct a 98% CI, this means that there is 1% for each
tail. The lower tail would be at 0.06 and the upper tail would be at (1 - 0.01) or
0.99. The closest to 0.94 on the z-table is between 0.9901 and 0.9898.
0.9898 corresponds with a z-score of 2.32.
0.9901 corresponds with a z-score of 2.33.
Taking the average of these two scores, we get a z-score of 2.325.
CONCEPT
Confidence Intervals
6
Sophia Introduction to Statistics Final Milestone
(Below is a compilation of all questions for Final Milestone. The answers are 100% correct, and it
guaranteed to earn you a perfect score in this unit. For a faster search, just hit on ctrl f on windows, or
command f on mac. Good luck!)
You passed this Milestone
25 questions were answered correctly.
1
What is the probability of NOT rolling a four when rolling a six sided die?
•
•
•
•
RATIONALE
Recall that the probability of a complement, or the probability of something NOT
happening, can be calculated by finding the probability of that event happening, and
then subtracting from 1. Note that the probability of rolling a four would be 1/6. So
the probability of NOT rolling a four is equivalent to:
CONCEPT
Complement of an Event
2
Select the following statement that describes non-overlapping events.
• Jon needs to roll an even number to win. When it’s his turn, he rolls a two.
• To win, Jon needs a red card. He receives a Queen of Diamonds.
• Receiving the King of Hearts fulfills Jon's need of getting both a face card and a
heart.
• Jon wants a face card so he can have a winning hand, and he receives the eight of
clubs.
RATIONALE
Events are non-overlapping if the two events cannot both occur in a single trial of a
chance experiment. Since he wants a face card {Jack, Queen or King} and he got
an eight {8}, there is no overlap.
, CONCEPT
Overlapping Events
3
Rob sent an email survey to 2,000 cell phone owners asking about their satisfaction
with their current plan. Only 256 people returned the survey and they were
predominately 18-24 years old.
Which of the following statements is true?
• The survey suffers from census issues because only 256 people responded.
• Rob included too many people on the survey list, affecting the data collected.
• Rob is ignoring the assumption that all survey participants will want to act
independently.
• The survey likely has bias because the people who could not answer differ from
those who did answer.
RATIONALE
In this survey there was a very low response rate with only 256 of the 2000. The
characteristics of those who responded are different from non-responders. Since the
responders and non-responders differ, we would worry about this affecting how they
responded.
CONCEPT
Bias
4
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of
customers follows a uniform distribution, a chi-square test for goodness of fit should be
performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest
hundredth.
• 0.67
,• 0.40
• 2.33
• 1.60
RATIONALE
Using the chi-square formula we can note the test statistic is
CONCEPT
Chi-Square Test for Goodness-of-Fit
5
What value of z* should be used to construct a 98% confidence interval of a
population mean? Answer choices are rounded to the thousandths place.
, • 2.055
• 2.325
• 1.175
• 1.645
RATIONALE
Using the z-chart to construct a 98% CI, this means that there is 1% for each
tail. The lower tail would be at 0.06 and the upper tail would be at (1 - 0.01) or
0.99. The closest to 0.94 on the z-table is between 0.9901 and 0.9898.
0.9898 corresponds with a z-score of 2.32.
0.9901 corresponds with a z-score of 2.33.
Taking the average of these two scores, we get a z-score of 2.325.
CONCEPT
Confidence Intervals
6
