STAT 1P98 – Written Assignment #2
Due Date: Thursday, June 30, 2022 @ 6:00 pm
The written assignment will be submitted digitally to Crowdmark. Use .pdf, jpg or png digital format for assignments.
– An email will be sent to your account to access Crowdmark
– Login with your Sakai student account
– For each question submit a photo or pdf of your solution. Each question is
uploaded separately and will accept multiple files for each question.
– When the assignment is completed, press Submit at the end of the page
– You can edit and change your answers up until the due date
– Please do not wait until last minute to submit your assignment as last-minute unforeseen events
do occur.
Show all your work for all questions, not just the final answer. Clearly label
your question parts, ie, part a), b), etc.
Question 1
A survey asked adult Americans (18 years or older) whether they used social
media regularly. The result shows in table below:
18 – 34 35 – 44 45 – 54 55 +
Use social media 117 89 83 49 Do not use social media 33 36 57 66
a). If an adult American is randomly selected, what is the probability he or she uses
social media?
b). If an adult American is randomly selected, what is the probability he or she is
45 to 54 years old?
c). If an adult American is randomly selected, what is the probability he or she is
35 to 44 years old and use social media?
d). If an adult American is randomly selected, what is the probability he or she is
35 to 44 years old or use social media?
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Question 2
Clarinex-D is a medication whose purpose is to reduce the symptoms associated
with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the
study experienced insomnia as a side effect. A random sample of 20 Clarinex-D
users is obtained, and the number of patients who experienced insomnia is
recorded. Use Excel or formula to complete the following questions a) to d).
a). Compute the probability that exactly 3 experienced insomnia as a side effect b). Compute the probability that 3 or fewer experienced insomnia as a side effect c). Find the probability that between 1 and 4 patients inclusive, experienced insomnia as a side effect. d). Would it be unusual to find 4 or more patients who experienced insomnia as a side effect? Why?
Question 3
Traffic fatalities occur at the rate of 1.32 fatal accidents per 100 million miles. Find
the probability that, during the next 100 million vehicle miles, there will be
a). Exactly zero fatal accidents. Interpret the result. b). A least one fatal accident. Interpret the result. c). More than one fatal accident. Interpret the result
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Question 4
Before every flight, the pilot must verify that the total weight of the load is less than the
maximum allowable load for the aircraft. The Bombardier Dash 8 aircraft can carry 37
passengers, and a flight has fuel and baggage that allows for a total passenger load of 6200 lb.
The pilot sees that the plane is full and all passengers are Adults. The aircraft will be overloaded
if the mean weight of the passengers is greater than 167.6 lb( 6200 / 37 = 167.6 lb). The
population body weights for 152 adults are in an Excel file on Sakai – Resources -Written
assignments.
a) Use Excel to calculate the population mean weights and standard deviation(stdev.p) for
152 adults. Keep the results in whole number. Submit a screenshot of Excel formula and
answer.
b) Use Excel to calculate the probability that the aircraft is overloaded – P( x > 167.6).
Submit a screenshot of Excel formula and answer.
c) Based on your result in part b), should the pilot take any action to correct for an
overloaded aircraft? Explain.
Question 5
In a survey of 1002 people, 70% said they voted in a recent presidential election. Answer the
following questions by hand.
a) 1002 people, how many of them said that they voted?
b) Use formula to construct a 82% confidence interval estimate of the proportion of the
people who say that they voted.
c) Use Brock calculator to construct a 97% confidence interval estimate of the proportion
of the people who say that they voted.
d) As the level of confidence increases what happens to the width of the confidence
interval?
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Question 6
You plan to develop a new software system that you believe will surpass the success of Google
and Facebook combined. In planning for the operating system that you will use, you need to
estimate the percentage of computers that use Windows. How many computers must be
surveyed in order to be 99% confident that your estimate is in error by no more than one
percentage point?
a) Assume that nothing is known about the percentage of computers with Windows
operating systems.
b) Assume that a recent survey suggests that about 90% of computers use Windows
operating systems (based on data from Net Applications).
c) Does the additional survey information from part (b) have much of an effect on the
sample size that is required?
Question 7
Students estimated the length of one minute without reference to a watch or clock and
the times (seconds) are listed below. Use a 0.05 significance level to test the claim that
these times are from a population with a mean equal to 60 seconds. Does it appear that
students are reasonably good at estimating one minute?
Estimate in sec 53 67 63 55 75 58
a) Write the null and alternative hypotheses.
b) Find critical values.
c) Calculate the test statistic by hand. Show your work, including all calculations.
At the 5% level, does it appear that students are reasonably good at estimating one
minute? Explain how you made that decision.
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Question 8
In a recent marathon with two races, 24,521 people in the first race finished and 283 dropped
out. In the second race, 12,853 people finished and 152 dropped out. Use a 0.05 significance
level to test the claim that the rate of those who finished is the same for both races.
a) State the null and alternative hypothesis b) Calculate the test statistic and find the critical value c) Test the claim by constructing an appropriate confidence interval. d) Based on the results from b) and c), do people finish the two marathons at the same
rate (proportion)?
Question 9
Listed below are self-reported heights and measured heights (in inches). Assume that
the paired sample data are simple random samples, and the differences have a
distribution that is approximately normal.
a. Calculate margin of error E using 97% confidence level.
b. Construct a 97% confidence interval estimate of the mean difference
between reported heights and measured heights.
c. Interpret the result of the confidence interval.
Reported Height Measured Height
68 67.9 71 69.9 63 64.9 70 68.3
71 70.3 60 60.6 65 64.5 64 67 54 55.6 63 74.2 66 65 72 70.8