mth 243 spring 2020 final exam (ice & snow)

histograms

mth 243 spring 2020 final exam (ice & snow)
● take your time
● do your best work
● make your processes clear
○ if you pick up your exam again three years from now and read it, you should beice & snow
able to understand what you did and why
● as you work, learn as much as possible about these techniques
● contact Ralf to discuss your questions!

1. Here are two histograms for “Data A” and “Data B.”
   Data A
   Data B
   Complete each statement using < (less than), > (greater than) or = (equal to).
   maximum(A) _ maximum(B) range(A) range(B)
   mean(A) mean(B) SD(A) SD(B)
   median(A) ___ median(B)
2. Here are the numbers (in thousands) of earned degrees in the United States in the
   2010–2011 academic year for students who are female or male. (And here’s a shout-out
   to all the non-binary and intersex people out there!)
   bachelor’s master’s professional doctorate total
   female 933 402 51 26 1412
   male 661 260 44 26 991
   total 1594 662 95 52 2403
   What’s the probability that a randomly selected degree earner
   a. is female?
   b. is female and the person has earned a professional degree?
   c. is female or the person has earned a professional degree?
   d. is female if the person earned a professional degree?
   e. earned a professional degree if the person is female?
3. Does the binary gender/degree data from the previous problem suggest that being
   female and earning a professional degree are
   a. Mutually exclusive events? How do you know?
   b. Independent events? How do you know?
4. The SAT and the ACT are tests used to measure “college readiness.” Math score
   distributions for both tests are unimodal and symmetric. In one recent year, The
   mathematics section of the SAT had a mean score of 515 and a standard deviation of
5. That same year, the math section of the ACT had mean 21.2 and standard
   deviation 5.7.
   Amanda took the SAT and Bita took the ACT. Amanda’s SAT math score was 775. Bita’s
   ACT math score was 33.
   Which student’s math score was more outstanding?
6. Avoiding an accident while driving can depend on reaction time. That time, measured
   from the moment the driver first sees danger until he or she steps on the brake pedal,
   follows an approximately normal distribution with a mean time of 1.5 seconds and a
   standard deviation of 0.18 of a second.
   a. What percent of drivers have a reaction time less than 1.25 seconds?
   b. What percent of drivers have reaction times between 1.6 and 1.8 seconds?
   c. What’s cut-off for the reaction times of the slowest 1/3 of all drivers, those drivers
   with the longest 1/3 of the reaction times?
7. (ice & snow problem: more data analysis practice) Here’s a systematic sample of 12
   statistics students’ face-to-face exam times (rounded to the nearest five minutes):
   45 60 75 75 75 85 90 90 95 100 105 130
   a. Calculate the five number summary
   i. min
   ii. Q1
   iii. median
   iv. Q3
   v. max
   b. Use technology (GeoGebra, etc.) to make a
   i. histogram
   (paste or draw it here)
   ii. boxplot
   (paste or draw it here)
   c. The statistics class is 110 minutes long. During the next quarter, the classroom
   needs to be used by another class after a 10-minute break. Should the instructor
   adjust the length of the exam? If so, why? If not, why not?
8. A carnival game offers a $100 cash prize for a game where the player tries to toss a ring
   onto one of many pegs. Alex will play the ring toss game five times, with an 8% chance
   of making any given throw. Notice there’s a set probability p and a set number n of
   attempts.
   a. What is the probability that Alex tosses one of the five rings onto a peg?
   b. What is the probability that Alex tosses more than one of the five rings onto a
   peg?
   c. If Alex tossed five rings again and again, how many rings would land on a peg on
   average, that is, what’s the mean number of successes he can expect?
9. In three math literacy classes, 42 out of 87 students reported their enrollment status as
   full-time. Their instructor, Jeff Lacks, would like to estimate the proportion of all math
   literacy students who are enrolled full-time with 95% confidence.
   a. Use Jeff’s data to construct a 95% confidence interval for the proportion of
   algebra students who are enrolled full-time. (Be sure to write a meaningful
   conclusion.)
   b. Jeff’s colleagues are interested in his results, but they’d like a more accurate
   estimate. To decrease his margin of error, how should Jeff adjust his
   i. sample size (while still using the confidence level 95%)?
   ii. confidence level (still with sample size n = 87)?
10. Census data for a certain county show that 19% of adult residents are Latin@s,
    Suppose 72 people are called for jury duty and only 9 of them are Latin@s. (Latin@ is
    shorthand for “Latina or Latino.”)
    Does this apparent underrepresentation of Latin@ people call into question the fairness
    of the jury selection process, that is, is there evidence that the proportion of Latin@
    people on the jury is less than we would expect if the selection process is fair?
    a. Write null and alternative hypotheses.
    b. Calculate the test statistic Z and the P-value.
    c. Does the data provide evidence that the process is unfair? Why?
11. Large herds of wild horses are a concern on some federal lands in the West.
    Researchers hoping to improve management of these herds collected data to see if they
    could predict the number of foals that would be born based on the size of the current
    number of adults in the herd. The research team recorded data on 38 herds of horses.
    Here is a scatterplot:
    Indicate which word, before or after the slash marks, makes each statement true.
    a. Association is… linear/nonlinear.
    b. Correlation is … weak/strong.
    c. Correlation is closer to … -1 / 0 / 1.
    d. On average, the number of foals decreases as the number of adults …
    increases/decreases.
    e. The slope of the regression equation tells you how many more foals are
    predicted to be in a herd with one … more/fewer … adult horse.
    ● take time to double check your results
    ● contact Ralf if you have any questions!
    Wow, you’ve completed MTH 243 Statistics I during the most challenging quarter in the recent
    history of academia. Congratulations! And thank you for all of your amazing work!
    <3 ralf and goblin grinch the statistics cat