Week 6 | Complete Solution

 Illowsky, et al. p. 400 #62

    62.     Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
    a.     If X ¯ = average distance in feet for 49 fly balls, then X ¯ ~ _______(_______,_______)
    b.     What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X ¯ . Shade the region corresponding to the probability. Find the probability.
    c.     Find the 80th percentile of the distribution of the average of 49 fly balls.

Illowsky, et al. p. 401 #70
    70.     Which of the following is NOT TRUE about the distribution for averages?
    a.     The mean, median, and mode are equal.
    b.     The area under the curve is one.
    c.     The curve never touches the x-axis.
    d.     The curve is skewed to the right.

Illowsky, et al. p. 406 #96
    96.     A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ tesst, what is the probability that the sample mean scores will be between 85 and 125 points?

Lane et al. p. 364 #4
    4.     Why is a 99% confidence interval wider than a 95% confidence interval?

Lane, et al. p. 365 #12
    12.     A person claims to be able to predict the outcome of flipping a coin. This
person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?

Lane  et al. p. 365 #15
    15.     You take a sample of 22 from a population of test scores, and the mean of your
sample is 60.
    (a)     You know the standard deviation of the population is 10.
What is the 99% confidence interval on the population mean.
    (b)     Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now?

Lane et al. p. 366 #18
    18.     You were interested in how long the average psychology major at your college
studies per night, so you asked 10 psychology majors to tell you the amount they study. They told you the following times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4.
    (a)     Find the 95% confidence interval on the population mean.
    (b)     Find the 90% confidence interval on the population mean

Illowsky, et al. p. 450 #100
    100.     What is meant by the term “90% confident” when constructing a confidence interval for a mean?
    a.     If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
    b.     If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.
    c.     If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
    d.     If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

Illowsky, et al. p. 452 #106
106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours.
    a.
        i.     x ¯ = __________
        ii.     sx = __________
        iii.     n = __________
        iv.     n – 1 = __________
    b.     Define the random variables X and X ¯ in words.
    c.     Which distribution should you use for this problem? Explain your choice.
    d.     Construct a 95% confidence interval for the population mean time wasted.
i.     State the confidence interval.
        ii.     Sketch the graph.
        iii.     Calculate the error bound.
    e.     Explain in a complete sentence what the confidence interval means.

Illowsky, et al. p. 454 #112
    112.     In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal.
    a.     Which distribution should you use for this problem? Explain your choice.
    b.     Define the random variable X ¯ in words.
    c.     Construct a 95% confidence interval for the population mean cost of a used car.
        i.     State the confidence interval.
        ii.     Sketch the graph.
        iii.     Calculate the error bound.
    d.     Explain what a “95% confidence interval” means for this study.