Sample Midterm Questions Stat 101

1. 27 people were interviewed and asked how many soft drinks they had consumed in the past month. The results:

23	34	0	4	41	8	42	8	67
50	1	16	10	20	82	5	31	21
46	11	39	3	18	51	18	63	24

(a) Make a stemplot of these data.

(b) Describe the overall shape of the distribution. Is it roughly symmetric, skewed to the right, or skewed to the left? Are there any outliers?

(c) Compute the five-number summary, the mean and standard deviation.

2. A study in Canada found that the distance from nose to outstretched fingertip of adult males varies according to a normal distribution with mean 903 mm and standard deviation 17 mm.

(a) What proportion of males have distance more than 880 mm?

(b) What is the distance that 90% of males exceed?

3. A study of two drugs (A and B) is to be carried out to determine whether they (alone or in combination) have an effect on disease X. 136 people with disease X are the subjects.

(a) Outline the design of the experiment.

(b) Use pseudorandom numbers from your calculator to choose the first 10 subjects for one group, after initializing the random number seed to 12345.

Death Anxiety	Religiosity
38	4
42	3
29	11
31	5
28	9
15	6
24	14
17	9
19	10
11	15
8	19
19	17
3	10
14	14
6	18

4. Researchers interested in determining if there is a relationship between death anxiety and religiosity conducted the following study. Subjects completed a death anxiety scale (high score = high anxiety) and also completed a checklist designed to measure an individuals degree of religiosity (belief in a particular religion, regular attendance at religious services, number of times per week they regularly pray, etc.) (high score = greater religiosity). It presumed that death anxiety was the explanatory variable. A data sample is provided at right:

1. Give the equation of the regression line.
2. Draw a scatterplot and the regression line (on the same plot).
3. What percent of the variability in religiosity is accounted for by the relation of these two variables?

(modified) Hour Exam 1 Stat 101 2007 summer

1. A study examined how long aircraft air-conditioning units operated after being repaired. Here are the operating times (in hours) for one unit:

97	51	11	4	141	18	142	68	77
80	1	16	106	206	82	54	31	216
46	111	39	63	18	191	18	163	24

(a) Make a histogram of these data, using 40-hour classes, starting with

0 ≤ time < 40, 40 ≤ time < 80, . . . .

(b) Describe the overall shape of the distribution. Is it roughly symmetric, skewed to the right, or skewed to the left? Are there any outliers?

(c) Is the five-number summary or the mean and standard deviation a better brief summary for this distribution? Explain your choice. Calculate the one of these summaries that you choose.

2. Biologists and ecologists record the distributions of measurements made on animal species to help study the distribution and evolution of the animals. The African finch Pyrenestes ostrinus is interesting because the distribution of its bill size has two peaks even though other body measurements follow normal distributions. For example, a study in Cameroon found that the wing length of male finches varies according to a normal distribution with mean 61.2 mm and standard deviation 1.8 mm.

(a) What proportion of male finches have wings longer than 65 mm?

(b) What is the wing length that only 2% of male finches exceed?

3. The drug AZT was the first effective treatment for AIDS. An important medical experiment demonstrated that regular doses of AZT delay the onset of symptoms in people in whom HIV is present. The researchers who carried out this experiment wanted to know the following:

• Does taking either 500 mg of AZT or 1500 mg of AZT per day delay the development of AIDS?

• Is there any difference between the effects of these two doses?

The subjects were 1200 volunteers already infected with HIV but with no symptoms of AIDS when the study started.

(a) Outline the design of the experiment.

(b) Use pseudorandom numbers from your calculator to choose the first 5 subjects for one group, after initializing the random number seed to 1347.

4. A long-term study of changing environmental conditions in Chesapeake Bay found the following annual average salinity readings in one location in the bay:

Year	1971	1972	1973	1974	1975	1976	1977
Salinity(%)	13.2	9.3	14.9	13.9	14.8	13.3	15.0
Year	1978	1979	1980	1981	1982	1983	1984
Salinity(%)	15.3	15.1	13.1	17.0	19.3	15.6	15.3

(a) Make a plot of salinity against time. Was salinity generally increasing or decreasing over these years? Is there an overall straight-line trend over time?

(b) What is the correlation between salinity and year? What percent of the observed variation in salinity is accounted for by straight-line change over time?

(c) Find the equation of the least-squares regression line for predicting salinity from year. Explain in simple language what the slope of this line tells you about this location in Chesapeake Bay.

(d) If the trend in these past data had continued, what would be the average salinity at this point in the bay in 1988?

Selected Answers:

1b. skewed right, no outliers (obviously no low outliers; max = 216 < 1.5*(111-18)+111 = 250.5, so no high outliers)

1c. 5-number summary is better because of the skew: min=1, Q1=18, median=54, Q3=111, max=216

2a. 0.0173813194

2b. 64.89674804 mm

3b. Number the volunteers 0-1199. The 1^st 5 are #324, 1077, 671, 61, 1166.

Selections (some modified) from Hour Exam 2 Stat 101 2007 summer

1. The weights of newborn children in the United States vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies a newborn as having low birth weight if the weight is less than 5.5 pounds.

(a) What is the proportion of U.S. babies weighing less than 5.5 pounds at birth?

(b) What weight do only 1% of U.S. newborns exceed?

(c) Without calculator approximate the weights between which the middle 68% fall.

2. Answer each of the following short questions.

(a) Give the upper 0.025 critical value for the standard Normal distribution.

(b) An opinion poll asks 1500 randomly chosen United States residents their opinions about relations with the nations of Europe. The announced margin of error for 95% confidence is ±3 points. But some people were not on the list from which respondents were chosen, some could not be contacted, and some refused to answer. Does the announced margin of error include errors from these causes?

Section Answers:

1a. 0.0547992894

1b. 10.40793485 lb.

1c. By the 68-95-99.7 rule, the middle 68% fall within 1 SD of the mean: 7.5-1.25 to 7.5+1.25 lb or 6.25 to 8.75 lb.

2a. 1.959963986

2b. No.

#	pts	of
1		30
2		30
3		15
4		25
tot		100

Midterm Stat 101 Name _____________

1. 10 students in Stat 101 were asked how many states they had visited. The results:

2

3

10

12

24

7

5

3

7

5

(a) Compute the five-number summary, IQR, the mean and standard deviation.

(b) Make a stem-and-leaf display of these data using split stems.

(c) Convert the stem-and-leaf display to a histogram.

(d) Draw a horizontal boxplot beneath the histogram with the same scale.

(e) Is the distribution roughly symmetric, skewed to the right, or skewed to the left? Are there any outliers?

Partial answers:

a. min = 2, Q1 = 3, median = 6, Q3 = 10, max = 24, IQR = 7, mean = 7.8, SD = 6.51153

b.

0 | 2 3 3

0 | 7 5 7 5

1 | 0 2

1 |

2 | 4

2 |

e. Skewed right. Note mean >> median, an indicator of right skew. 24 is a high outlier.

Height	Shoe
69	10.5
68	12
71	14
67	10
68	10
72.5	10.5
67	10.5
72	10.5
68	9
73	12

2. 10 male students in Stat 101 were queried about their height and shoe size. The results are in the table at right. Assume Height is the explanatory variable.

a) Give the equation of the regression line (use 5 decimal places).

b) Draw a scatterplot and the regression line (on the same plot).

c) What proportion of the variability in shoe size (use 5 decimal places) is accounted for by the linear regression model?

d) Find the data point with the largest residual and state that residual (use 4 decimal places).

e) What shoe size does this model predict for a height of 70 inches?

f) Do you think this is a good model? Why or why not?

Answer:

a. shoe^ = -6.47867+0.24987height

c. 0.17170

d. (71, 14); residual = 2.7377

e. 11.01244

f. With a scatterplot not looking very linear, and R² = 0.17170 (r = 0.41437) showing rather weak association, this is not a good model.

3. A small pilot study of two dosage levels of aspirin (81 mg/day and 162 mg/day) is to be carried out to help determine whether a larger study will be done later to try to find an effect on heart disease. 15 people with heart disease are the subjects.

(a) Outline the design of the experiment.

(b) Use calculator-generated pseudorandom numbers with random number seed initialized to 142 to choose the subjects for one group. Number the subjects 0-14.

Answer:

a.

random assignment 5 subjects – 162 mg/day -----

/ \ evaluate

15 subjects --- 5 subjects – 81 mg/day -------- and

\ / compare

5 subjects – placebo ---------

b. randInt(0,14,5) gives 13, 8, 0, 9, 7

4. The weights of newborn children in the United States conform closely to a normal model with mean 7.5 pounds and standard deviation 1.25 pounds.

(a) What is the proportion of U.S. newborns weighing between 7 and 9 pounds at birth?

(b) What is the weight that only 10% of U.S. newborns exceed?

(c) What weight has a z-score of -2?

(d) What is the z-score of a weight of 10 lb.?

(e) Between which weights do the middle 90% of U.S. newborns fall?

Answer:

1. normalcdf(7,9,7.5,1.25) gives 0.54035
2. invNorm(.9,7.5,1.25) gives 9.10194 lb.
3. 5
4. 2
5. invNorm(.05,7.5,1.25), invNorm(.95,7.5,1.25) give 5.44393 lb., 9.55607 lb.