Examination — Statistics: From Data to Decisions

1.A hospital records each arriving patient's triage category — green, yellow, orange, or red, in increasing order of urgency. What kind of variable is the triage category?

2.Find the median of 14, 9, 21, 6, 11, 17.

3.For the sorted data 5, 8, 11, 12, 15, 19, 22, find the interquartile range (Q3 − Q1).

4.A dataset has a mean of 46 and a median of 58. What does this reveal about the shape of the distribution?

5.Match each variable to its level of measurement.

6.Battery lifetimes are normal with a mean of 40 hours and a standard deviation of 5 hours. About what percent last between 30 and 50 hours? Enter a whole number.

7.For those same batteries — normal, mean 40 hours, standard deviation 5 hours — about what percent last less than 45 hours?

8.A value of 63 comes from a distribution with mean 75 and standard deviation 8. Find its z-score.

9.A newborn's birth weight has a z-score of −2.3 in a roughly normal distribution of birth weights. How should a clinician read this value?

10.A radio station runs an online poll open to anyone who wishes to answer, and 5,000 people respond. In one sentence, explain why this large sample can still misrepresent the wider public.

11.Drawing random samples from one fixed population, order these sample sizes by how much the sample mean varies from sample to sample — from the most variable to the least.

1. ⋮⋮A sample of size 25 ↑ ↓
2. ⋮⋮A sample of size 100 ↑ ↓
3. ⋮⋮A sample of size 400 ↑ ↓

12.A population has a standard deviation of σ = 60. Find the standard error of the mean for a sample of size 144.

13.A sample gives an estimate of 68% with a standard error of 3%. Using a multiplier of 2 for 95% confidence, what is the upper end of the confidence interval, in percent?

14.A 95% confidence interval for a candidate's support runs from 44% to 50%. A commentator declares the candidate 'certain to fall short of a majority.' Is that justified?

15.A scatterplot of a car's age (across) and its resale value (up) shows points falling steadily from the upper left to the lower right, hugging a straight line. Describe the relationship.

16.Four points have z-score products of 0.9, 0.7, 0.6, and 0.8. Using r = (sum of the z-score products) ÷ (n − 1) with n − 1 = 4, find r.

17.A relationship has r = 0.6, with s_x = 5 and s_y = 20. Find the regression slope b = r · (s_y / s_x).

18.A study finds that towns with more bookstores have higher average test scores. A columnist concludes that bookstores raise test scores. What is the most sensible reading?

19.A profit figure rises from 200 to 206. A chart crops its vertical axis to begin at 198, so the two bars stand 2 and 8 units tall. How many times taller does the second bar look than the first?

20.To test whether a new tutoring program raises grades, which design best supports a claim that the program CAUSES the improvement?

21.Without looking back: name the four stages of the critical checklist in order, and state which stage sets the ceiling on your confidence in a conclusion.