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Please attach a cover sheet (posted on Connect) when you hand in the assignment.
Due: Friday Aug 4 at 1pm in the STAT200 dropbox in ESB (No late homework will be accepted)
Total marks: 30 marks
Instructions:
• Typewritten answers are preferred. If your handwriting is illegible or if the answers are not presented
in a neat and organized manner, with answers clearly numbered you may lose marks.
• If you use R Commander to compute probabilities for any of the questions, please state clearly that you
have done so and provide parameter values that you input in R Commander.
1. As a statistician, you are asked to give advice on designing a volunteer appreciation event for a local
charity. They plan to put one blue ball and a number of red balls in a black box, let a volunteer draw
a ball from the box and award a Starbucks gift card if the volunteer draws the blue ball. They want
advice on how many red balls they should put in the box. There will be 400 volunteers attending the
event. Their initial plan is to put one blue ball and 9 red balls in the black box.
(a) Under the charity’s initial plan, identify the mean and the standard deviation of the proportion of
the volunteers who manage to pick the blue ball among 400 volunteers. [1 mark]
(b) Under the charity’s initial plan, how many gift cards they should prepare in order for the number
of prepared gift cards to be enough with at least 97.5% probability to award every volunteer who
picks the blue ball? [2 marks]
(c) The charity wants 50 gift cards to be enough with at least 97.5% probability to award every volunteer
who picks the blue ball. Find the minimum number of red balls they should put in the box in order
to satisfy this criterion. [3 marks]
2. Wildlife scientists studying a certain species of frogs know that past records indicate the adults should
weigh an average of 118 grams with a standard deviation of 14 grams. One of the scientists fears that
environmental changes may be adversely affecting the frogs. The researchers collect a random sample
of 50 adult frogs and weigh them. In their sample the mean weight was 112 grams. Do you think this
sample result is unusually low? Explain. [3 marks]
3. The dataset ExerciseHours comes from an in-class survey of randomly sampled statistics students at a
certain college asking about amount of exercise, TV viewing, handedness, gender, pulse rate, and number
of body piercings. The dataset contains 50 observations with the following 7 variables:
Year Year in school (1=First year,…, 4=Senior)
Gender F or M
Hand Left (l) or Right (r) handed?
Exercise Hours of exercise per week
TV Hours of TV viewing per week
Pulse
Resting pulse rate (beats per minute)
Pierces
Number of body piercings
(a) Create a 95% confidence interval for the mean hours of exercise a week for all statistics students at
this college. [2 marks]
(b) Suppose nationally, college students spend an average of 5 hours exercising a week. Is there evidence
to conclude that the mean weekly hours of exercise of all statistics students at this college is
significantly different than the national weekly average hours of exercise? Use your confidence
interval in part 3a to test the appropriate hypothesis. Be sure to clearly state your hypotheses and
conclusion in the context of the question. [3 marks]
1 (c) State any assumptions/conditions necessary in the context of the question. [1 mark]
4. Distracted driving (such as texting while driving) can increase the chance of a motor vehicle crash.
A new report states that 31% of drivers read or send texts while driving. Suppose that road safety
organization randomly sampled 300 teenagers, of whom 120 reported that they read or sent texts while
driving in the last month. Does this indicate that distracted driving is more severe among teenagers?
(a) Identify the population of interest. [1 mark]
(b) State the hypotheses. Define all your notation. [2 marks]
(c) Compute the test statistic. Make sure to clearly state all assumptions in the context of the question.
[3 marks]
(d) Find the exact value or provide a range of values for the P-value. Sketch your model and shade the
corresponding region (a sketch by hand is fine). [2 marks]
(e) At the 1% significance level, state your conclusion for the hypothesis test in the context of the
question. [1 mark]
(f) Based on your conclusion above, what type of error are you at risk of making? Explain your answer
in the context of this question. [2 marks]
(g) Construct a 95% confidence interval for the parameter you identified in part (a). [2 marks]
(h) Suppose the researcher plans to re-estimate of the proportion of teenagers who text while driving
and wants the estimate to be correct within 0.06 with 99% confidence. Approximately how large a
sample would be required? [2 marks] 2
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