Name:______Date:______
Labouré College
Essentials of Statistics
MAT3401
ANSWERS
Final Prep
Questions from Chapter 1
You are conducting a study of nurses working at Hospital Q. You plan to take a sample and give them a survey. Among the questions on your survey instrument are:
A. How many hours are you scheduled to work each week? Answer to the nearest hour.______
B. How satisfied are you with the number of hours of work you have scheduled per week? Respond using the following scale: 1 = not at all, 2 = somewhat, 3= very
1. How would you classify variable A above? Circle one answer (1 point).
- It is a qualitative, nominal variable. (not qualitative, which is category)
- It is a qualitative, ordinal variable. (not qualitative, which is category)
c. It is a quantitative, ratio variable.
d. It is a quantitative, nominal variable. (not nominal, which is category)
2. How would you classify variable B above? Circle one answer (1 point).
- It is a qualitative, nominal variable. (not equal categories)
b. It is a qualitative, ordinal variable. (has an “ord”er of increasing satisfaction)
- It is a quantitative, ratio variable. (not quantitative; categories instead)
a. It is a quantitative, nominal variable. (not quantitative; categories instead)
3. Is the proportion of responses “3 = very” to question B a statistic or a parameter? Circle one answer. (1 point)
a. Statistic (from a sample – see question)
b. Parameter (from a population)
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4. Suppose you take random samples (not the whole population) from the following nurse occupational classifications at Hospital Q: Nurse I, Nurse II, Nurse III, Supervising Nurse I, and Supervising Nurse II. Most nurses (80%) fall in the Nurse I and Nurse II categories, but you want to get a good representation of higher level and supervising nurses, too. Therefore, you choose to send 20% of your surveys to nurses in each category so each one is equally represented (since there are 5 categories, each category will be represented equally and equal 100%). What kind of sampling technique are you using? Circle one answer. (1 point)
a. Simple random (not equal chance of being sampled)
b. Stratified (divided into categories or “strata” then sampled)
c. Systematic (taking every “nth” in the sample)
d. Cluster (geographic)
e. Multistage (several stages of sample – large studies)
f. Convenience (already-gathered group: class, participants at an event, etc.)
5. Of the population of 150 nurses working at Hospital Q, you only sampled 30 of them (6 from each category). From your sample of 30, you calculate a mean age of nurses of 47.8. Is 47.8 a parameter or a statistic? Circle one answer (1 point).
- 47.8 refers to a parameter. (this was not from a population)
b. 47.8 refers to a statistic. (from a sample)
6. The Human Resources Department at Hospital Q tells you that, over 2012, among the entire population 150 nurses, 15 (10%) were promoted to a higher job classification. Is 10% a parameter or a statistic? Circle one answer (1 point).
a. 10% refers to a parameter. (from the population – see question)
b. 10% refers to a statistic. (this was not from a sample)
7. You want to test your job satisfaction survey. Labouré College gives you permission to distribute your survey to a microbiology class that includes 25 nursing students. You attend the class once and administer the survey. What type of sampling are you using? Circle one answer (1 point).
- Cluster (geographic)
- Simple random sampling (randomize list)
- Stratified (divide into “strata” first then sample)
- Convenience (already-assembled group)
8. Imagine you send out your survey to your sample of nurses by e-mail to their work e-mail. You send it out on December 24 (day before Christmas) and say they must fill it out before 7 days is up, which is December 31 (New Year’s Eve). You know from experience the organization only has a few nurses on staff during that week, as most nurses take time off. What kind of mistake might you be making? Circle one answer (1 point).
a. Undercoverage
- Faulty recall
- Hidden bias
- Interviewer influence
9. An OB/GYN clinic wants to study the health of babies born to mothers who are HIV positive. The mother is enrolled in the study when it is found she is HIV positive and pregnant, and then is contacted to complete several surveys during the prenatal period, when the baby is born, and one year after the baby is born. What type of study design is this? Circle one answer (1 point).
a. Observational study (no intervention)
- Experiment (intervention needs to be given)
10. An investigator wants to study if a new drug approved for Alzheimer’s disease can actually improve memory in young people. The investigator enrolls 50 college students, and randomizes 25 to receive placebo, and 25 to receive the Alzheimer’s drug. Then, she tests the students to see if those in the drug group are able to memorize items more quickly than those in the placebo group. What type of study design is this? Circle one answer (1 point).
- Observational study (not the type with an intervention)
b. Experiment (intervention is drug/placebo)
Questions from Chapter 2
1. The following data represent the observed number of native plant species from random samples of study plots on different islands in the Galapagos Island chain.
Reference: Science, Vol. 179, p 893-895.
23 26 33 73 21 35 30 16 3 17
9 8 9 19 65 12 11 89 81 7
23 95 4 37 28
Select the correct stem-leaf that describes the plant species data by circling the letter corresponding to the correct stem-leaf plot. (2 points)
a.
b.
B is the correct answer
c.
d.
2. Identify the shape of the distribution for the plant species data (1 point).
Skewed right
3. In a survey you conducted, you asked 100 respondents to rate how much they liked spiders on a 1 to 5 scale, where 1 means “not at all” and 5 means “a lot”. You found that respondents were pretty polarized on the issue – they either really did not like spiders, or they loved them. Which histogram below represents this type of finding? Circle the letter corresponding to the correct histogram. (2 points)
a.
b. B is the correct answer.
c.
d.
Questions from Chapter 3
The following is a box and whisker plot for the result of science test scores in a class.
1. Is the minimum score less than 50? Circle the correct answer below. (1 point)
a. The minimum score is less than 50.
b. The minimum score is equal to 50.
c. The minimum score is more than 50.
2. Is the maximum score more than 90? Circle the correct answer below. (1 point)
a. The maximum score is more than 90.
b. The maximum score is equal to 90.
c. The maximum score is less than 90.
3. What is the value of Q1? Circle the correct answer below. (1 point)?
a. 54
b. 73
c. 81
d. 90
e. 95
4. What is the value of Q3? Circle the correct answer below. (1 point)?
a. 54
b. 73
c. 81
d. 90
e. 95
Suppose you wanted to compare 3 lathes that make motor shafts to a design specification. The shafts are supposed to be 18.85 mm when they are done. You create a sample of motor shafts for each lathe (Lathe 1, Lathe 2, and Lathe 3), measure the shafts, and plot them below to compare. (From ASQ.org.)
1. Which group of lathe had the highest median of shaft size? Circle the letter for the correct answer. (1 point)
a. Lathe 1
b. Lathe 2
c. Lathe 3
2. Which lathe had the largest range of shaft sizes ? Circle the letter for the correct answer. (1 point)
a. Lathe 1
b. Lathe 2
c. Lathe 3
3. Which lathe had the largest interquartile range of shaft sizes ? Circle the letter for the correct answer. (1 point)
a. Lathe 1
b. Lathe 2
c. Lathe 3
The Maui News gave the following costs in dollars per day for a random sample of 20 condominiums located throughout the island of Maui:
For Questions 8-10, round to 1-digit after the decimal.
89 50 68 60 375 55 500 71 40 350
60 50 250 45 45 125 235 64 60 130
4. What is the mean of the above data ? Circle the letter for the correct answer. (1 point)
a. $50.85
b. $97.35
c. $136.15 (2,723/20) = 136.15
d. $182.45
5. What is the median of the above data? Circle the letter for the correct answer. (1 point)
a. $66.50 (10th and 11th place are 65 and 68. (65+68)/2 = 133/2 = 66.5)
b. $82.70
c. $145.55
d. $220.25
6. What is the mode of the above data? Circle the letter for the correct answer. (1 point)
a. $40
b. $45
c. $50
d. $60 (occurs 3 times)
7. Imagine you learned that the standard deviation of the above data was $133.56. You also learned that the standard deviation for a random sample of 20 costs in dollars per day of condominiums to rent in Boston was $182.45. Which city has more variation in its costs? Circle the letter for the correct answer. (1 point)
a. Maui has more variation than Boston.
b. Boston has more variation than Maui. ($182.45 is higher than $133.56)
c. Neither, they have equal variation.
Questions from Chapter 4
See the scattergram below and answer several questions.
1. What kind of association is shown between x and y in the scattergram? Circle the letter for the correct answer. (1 point)
a. Positive correlation (trend going upward)
b. Negative correlation (trend going downward)
c. No correlation (no trend)
2. What kind of association is shown between x and y in the scattergram? Circle the letter for the correct answer. (1 point)
a. Strong
b. Moderate
c. Weak
d. None
3. What is the value of the correlation coefficient between x and y? You should be able to pick out the right answer from the list from looking at the scattergram. Circle the letter for the correct answer. (1 point)
a. -0.02 (negative is correct direction, but weak correlation so not correct)
b. 0.75 (not correct – correlation not positive)
c. -0.89 (strong, negative correlation)
d. 0.84 (not correct – correlation not positive)
4. What is the equation for the least squares line? You should be able to pick out the right answer from the list from looking at the scattergram. Circle the letter for the correct answer. (1 point)
a. y-hat = -0.8x + 33.3 (correct – sign of slope (b) same as sign of correlation (r))
b. x-hat = -0.8y + 33.3 (never predicting x-hat. y-hat is dependent variable)
c. y-hat = 0.8x + 33.3 (not correct – sign of slope (b) positive, must be negative if negative correlation r)
d. x-hat = 0.8x + 33.3 (never predicting x-hat. y-hat is dependent variable)
5. Imagine x = 10. Using the equation, predict y-hat. (1 point)
a. 23.4
b. 14.6
c. 33.3
d. 25.3 see answer a to question 4 above: (-0.8)(10)+33.3 = 25.3
Questions from Chapter 7
· Researchers asked Japanese people in Ohasama to measure their blood pressure every day as part of a study and report back what they measured.
· After the study was done, the researchers found that for the systolic blood pressure (SBP), μ=117.3 mmHg and ϭ=13.4 mmhg
· Source: Imai, Y., et al. (1993) Characteristics of a community-based distribution of home blood pressure in Ohasama in northern Japan. J Hypertension 11(12):1441-1449.
Answer the following questions based on this population’s SBP, where systolic blood pressure (SBP), μ=117.3 mmHg and ϭ=13.4 mmhg.
Round SBPs to 1-digit after the decimal.
Round Z scores to 2-digits after the decimal.
Round probabilities/p-values to 4-digits after the decimal.
Round percentages to a whole number.
1. According to the Empirical Rule, what is the SBP cutpoint for 34% of the data above the mean? (1 point)
a. 103.9
b. 117.3
c. 130.7 34% is 1 ϭ above μ. 117.3 + 13.4 = 130.7.
d. 117.0
2. According to the Empirical Rule, what is the SBP cutpoint for 34% of the data below the mean? (1 point)
a. 103.9 34% is 1 ϭ below μ. 117.3 - 13.4 = 103.9.
b. 117.3
c. 130.7
d. 117.0
3. What is the z-score for the probability that, for an Ohasama resident selected at random, x is greater than 119.2? Circle the letter for the correct answer. (1 point)
a. -1.14
b. 0.14 (119.2 – 117.3)/13.4 = 0.14
c. -0.5557
d. 0.4443
4. What is the probability that, for an Ohasama resident selected at random, x is greater than 119.2? Circle the letter for the correct answer. (1 point)
a. -1.14
b. 0.5557
c. 0.4443 Look up 0.14 in z table, which is 0.5557 – which is bigger than 50%. The question asks for likelihood of being greater than 119.2, and since μ is below that at 117.3, we are looking for <50% piece at top. Therefore, 1 – 0.5557 = 0.4443. Best to draw a picture.
117.3 119.2
d. 0.0145
5. What is the probability that, for an Ohasama resident selected at random, x is less than 115.4? Circle the letter for the correct answer. (1 point)
a. 0.5557
b. 0.4443 Same situation as Question 4 – you need a picture to see that since you get this when you look up the z score for -0.14, you keep it since it is <0.5000 (50%) and you are looking for the little piece. You don’t need to do the 1 minus thing. Draw a picture!
115.4 117.3