Statistical Analysis

Instructions: All answers must be written or typed up only in the space provided. Calculations must be
shown for every numerical problem in order to get full credit for it. Partial credit will be given where
appropriate.


  1. Please refer to the population distribution in the graph below.
    a. Is the above distribution left-skewed, right-skewed or symmetric? (2 points)
    b. Without performing any calculations, state with justification which value is greater in the
    distribution above: the mean or the median? (2 points)
    c. Would it be appropriate to apply the Empirical Rule to this distribution? Why or why not?(2
    points)
    d. Given that the mean of this distribution is 39 and standard deviation is 5, what percent of
    data values lie between 28 and 50? (4 points)
  2. A random sample of people from three age groups were asked to describe their general
    stress level. The three age groups were Young Adult (18-35 years), Middle-Aged Adult
    (36-55 years) and Older Adult (>55 years). The stress levels were High, Medium, Low and
    None. These responses were classified into the following table. Use the data from this table
    to answer the questions below.
    0 .02 .04 .06 .08 .1
    Density
    20 30 40 50 Income
    Age Group
    a. What is the probability that a person selected at random feels no stress or has a low stress
    level? Which rule did you use to answer this question? (3 points)
    b. What is the probability that a person selected at random has a high stress level, given that
    this person is an older adult? (2 points)
    c. What is the probability that a person selected at random is a young adult and has a low
    stress level? (2 points)
    d. What is the probability that a person selected at random is a middle-aged adult or has a
    medium stress level? Which rule did you use to answer this question? (3 points)
  3. There is a 19% chance that an RT-PCR virus test will return a false negative (i.e., falsely
    indicate negative for the virus). 16 people are administered this test in a particular session. A
    test either returns a false negative or it does not. The probability of one test returning a false
    negative is independent of the probability of any other test returning a false negative.
    Stress Level Young Adult Middle-Aged Adult Older Adult
    High 13 19 9
    Medium 18 23 6
    Low 10 18 5
    None 12 7 10
    a. What is the probability of at least one of the tests administered during this session returning
    a false negative? (6 points)
    b. What is the expected number of false negatives returned in this session? (3 points)
    c. What is this type of problem (i.e. distribution) called as? Justify your answer. (2 points)
  4. The length of Zoom class sessions at a university is normally distributed, with a mean of 76
    minutes and a standard deviation of 27 minutes.
    a. What is the probability of a Zoom class session at this university being greater than one
    hour? (3 points)
    b. What is the probability of a Zoom class session at this university being greater than two
    hours? (3 points)
    c. How long does a Zoom session at this university need to be for it to be in the top 5% longest
    Zoom sessions? (4 points)
  5. Donald Trump received 43.25% of the votes cast in Colorado in the 2016 presidential
    election. A random sample of 275 likely voters in Colorado showed that 107 of them were
    going to vote for him in the 2020 presidential election. At the 5% level of significance, can
    we conclude that the proportion of Colorado voters voting for Donald Trump is significantly
    lower in 2020 than it was in 2016? Use this given data to answer the questions below.
    a. State the null and alternate hypotheses. (1 point)
    b. What is the decision rule? (2 points)
    c. What is the test statistic (and what is its value)? (3 points)
    d. What is the decision? Interpret this decision in 1 sentence. (2 points)
    e. What is the p-value? (2 points)
  6. Open a blank Excel spreadsheet and enter the following sample values in the first column
    (column A), starting in cell A1. Each value denotes the number of minutes a sample
    respondent indicated they spent waiting in line to vote in an election in person.
    77, 55, 30, 62, 51, 30, 15, 63, 74, 83, 19, 81, 35, 21, 65, 62, 43 and 68.
    a. Write down the Excel formulas used to calculate the mean and standard deviation of this
    sample. (2 points)
    b. What are the mean and standard deviation of this sample (as obtained using Excel)? (2
    points)
    c. Calculate the 95% confidence interval for the average amount of time a person spent
    waiting in line to vote. (2 points)
    d. Assume that another random sample of 25 people gave you the same mean and standard
    deviation as obtained in part (b). Calculate the new 95% confidence interval for the average
    amount of time a person spent waiting in line to vote. Explain in 1-2 sentences why this new
    95% C.I. is wider or narrower than the one calculated in part (c). (3 points)
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