STAT 1350 Review for Midterm
1. An overnight opinion poll calls randomly selected telephone numbers. This polling method misses all people without a telephone.
a) Is this a source of nonsampling error or of sampling error?
Sampling error – undercoverage (misses all people without a telephone) OR nonsampling error – overnight calls, nonresponse
b) Does the poll’s announced margin of error take this source of error into account?
No, the margin of error only measures random sampling errors.
2. On September 7, 2007, 384 professional golf fans were asked “Do you think that, as a result of becoming a father, Tiger Woods’s golf game will improve, not be affected, or will get worse?” In all, 70% said “not be affected.”
a) What is the population for this survey? All golf fans
b) Use the quick method to find the margin of error.= 5%
c) Give a complete confidence statement for a conclusion about the population.
We are 95% confident that 70% of all golf fans feel Tiger Woods’s golf game will net be affected with a margin of error of + 5%.
3. A Washington Post article reported a study comparing the effectiveness of three common painkillers for children. Three hundred children, aged 6 to 17, were randomly assigned to four groups. Group A received a standard dose of ibuprofen. Group B received a standard dose of acetaminophen. Group C received a standard dose of codeine. Group D received a placebo. The youngsters rated their pain on a 100 point scale before and after taking the medicine.
a) Outline the design of this experiment.
b) Identify the subjects of this experiment:
300 children aged 6 to 7
c) Identify the explanatory variable:
drug used – ibuprofen, acetaminophen, codeine, placebo
d) Identify the response variable:
level of pain on scale of 1 to 100
e) You read that this was a double blind experiment. Explain what that means in this situation.
The subjects (children) do not know which of the treatments they are assigned and the researchers who are measuring the response variable do not know the treatment the subjects received when they record the level of pain.
f) You also read that there was a significantly greater decrease in pain ratings for Group A than for Groups B, C and D, but there was no significant difference in the decrease of pain ratings for Groups B, C and D. What does this mean?
Ibuprofen is more effective than the other treatments in decreasing the level of pain.
g) What does this finding lead you to conclude about the use of ibuprofen as a painkiller?
Ibuprofen is the best painkiller to use for reducing pain.
Here are boxplots of the number of calories in 20 brands of beef hot dogs, 17 brands of meat hot dogs, and 17 brands of poultry hot dogs.
4. / The main advantage of boxplots over stemplots and histograms isA) / boxplots make it easy to compare several distributions, as in this example.
B) / boxplots show more detail about the shape of the distribution.
C) / boxplots use the five-number summary, whereas stemplots and histograms use the mean and standard deviation.
D) / boxplots show skewed distributions, whereas stemplots and histograms show only symmetric distributions.
5. This plot shows that
A) / all poultry hot dogs have fewer calories than the median for beef and meat hot dogs.
B) / about half of poultry hot dog brands have fewer calories than the median for beef and meat hot dogs.
C) / hot dog type is not helpful in predicting calories, because some hot dogs of each type are high and some of each type are low.
D) / most poultry hot dog brands have fewer calories than most beef and meat hot dogs, but a few poultry hot dogs have more calories than the median beef and meat hot dog.
6. We see from the plot that the median number of calories in a beef hot dog is about
A) 190. B) 179. C) 153. D) 139. E) 129.
7. The box in each boxplot marks
A) / the full range covered by the data.
B) / the range covered by the middle half of the data.
C) / the range covered by the middle three-quarters of the data.
D) / the span one standard deviation on each side of the mean.
E) / the span two standard deviations on each side of the mean.
8. The calorie counts for the 17 poultry brands are:
129 132 102 106 94 102 87 99 170 113 135 142 86 143 152 146 144
a) What is the mean and the standard deviation for this data?
Mean = 122.47Standard Deviation = 25.48
b) What is the five number summary for this data?
Min x = 86
Q1 = 100.5
Med = 129
Q3 = 143.5
Max = 170
9. For a distribution that is skewed to the left, usually
A)the mean will be larger than the median.
B)the median will be larger than the mean.
C)the first quartile will be larger than the third quartile.
D)the standard deviation will be negative.
E)the minimum will be larger than the maximum.
10. For a distribution that is skewed to the right, usually
A)the mean will be larger than the median.
B)the median will be larger than the mean.
C)the first quartile will be larger than the third quartile.
D)the standard deviation will be negative.
E)the minimum will be larger than the maximum.
11. For a normal distribution with mean 20 and standard deviation 5, approximately what percent of the observations will be between 5 and 35?
99.7%
12. For a normal distribution with mean 20 and standard deviation 5, approximately what percent of the observations will be less than 20?
50%
13. For a normal distribution with mean 20 and standard deviation 5, approximately what percent of the observations will be less than 10?
2.5%
14. The distribution of heights of adult men is approximately normal with mean 69 inches and standard deviation 2.5 inches. How tall is a man whose standardized height is z = –0.3 ?
68.25 inches
15. Scholastic Assessment Test (SAT) scores are normally distributed with mean 500 and standard deviation 100. Jason scores 440 on the math SAT. Jason's standard score is:
–0.6.
16. Suppose that adult women in China have heights that are normally distributed with mean 155 centimeters and standard deviation 8 centimeters. Adult women in Japan have heights which are normally distributed with mean 158 centimeters and standard deviation 6 centimeters. Which country has the higher percentage of women taller than 167 centimeters?
The percentages are the same.