Practice Questions for Exam I And Homework #3Questions 1 and 2. A researcher is interested in the averageQuestion 3. Suppose a water sample is collected from a monitQuestion 9. In a study of the effect of automobile exhaust oQuestion 10. Suppose you are on a team of researchers studyQuestion 11Here are the statistics and a stem and leaf plot for 39 obseMaximum 1920.0Median 1410.0Minimum 1180.0Mean 1444.62Std Dev 183.13N 39Variance 33536.032CV 12.677Question 12. A farm manager has 30 calves recently weaned frPractice Questions for Exam I And Homework #3 Assignment for HW # 3: due Tuesday, 30 September, at the start of the lecture. Please submit answers for questions 13 through 17. The answers to all questions will be made available after the lecture on the 30th. Questions 1 and 2. A researcher is interested in the average number of parasitic fish found attached to a certain species of shark. Because sharks are not easy to come by, the researcher was able to collect data for only 6 sharks. The numbers of parasitic fish per shark were 5, 3, 9, 16, 7, 3. 1. The median for this data is a. 9 b. 12.5 c. 6 d. 7 2. True or False: a. the median is the more appropriate measure of center because there is a large outlier b. the mean is a more appropriate measure of center because it is a small data set c. if the researcher subtracted the value of 3 from every observation, then the large value would not be quite so big and the mean would now be appropriate to describe the center of this data d. the researcher should use the mode of 3 as the best measure of center Question 3. Suppose a water sample is collected from a monitoring station in the Choptank River on a regular basis and Dissolved oxygen (DO) is measured. In May, the DO value observed was 5.1 mg/l and in July it was 3.7 mg/l. Now, the observation from May was a single selection from a population of DO values that are normally distributed with a mean of 8.0 mg/l and a standard deviation of 2.6. The July measurement was taken from a Normal Distribution with a mean of 8.0 mg/l and a standard deviation of 4.3. Which is the more unusual value for its sampling time, the 5.1 in May or the 3.7 in July? Show any work and explain your choice. The 5.1 May value is 1.115 standard deviation units below the mean of 8 whereas the 3.7 July value is exactly 1 standard deviation unit below the mean of 8. Hence, the 5.1 mg/l in May is a more unusual value than the 3.7 mg/l is in July. Note that the difference is due to the variability seen in July, which is very much larger than the variability in May. Question 4. For each entry in the following list, identify the type of variable as either categorical (CA), discrete (D), or continuous (CO) a) Number of bacterial colonies on an agar plate CA D CO b) Forage grass biomass per square meter (kg/m2) CA D CO c) Burrowing depth of an insect (mm) CA D CO d) Insect Species CA D CO e) Time until first molt of a newly emerged caterpillar CA D COf) Number of species of grass in a square meter CA D CO g) Age at diagnosis of disease for a patient (years) CA D CO* h) Lead exposure status (yes, no) of a child in a household CA D CO *the answer depends on how age is recorded – if it is as whole years then it is discrete but if it is as years+months+days then it could be considered continuous. Question 5. See the graph below. Two hundred just weaned calves were randomly allocated to one of seven feed diets and monthly weight gain data (lbs) was collected. The accompanying figure shows box plots of the data for each diet treatment. Which of the diets would you recommend the farmer use in future? Briefly, explain your choice. 1 2 3 4 5 6 7DIET010203040506070WGHTGAIN There are two possible choices here. The best is diet 6 because it has the highest median. A second best choice could be diet 7 because although it’s median is not the highest (only second highest) it does have the highest 75th percentile. Diets 1, 2, and 3 are clearly poor choices because the values in the middle 50% are too low. Diet 4 might be ok if there were not diets 6 and 7. Finally, diet 5 is out because it is too variable and the middle 50% is too low in value. Questions 6, 7 and 8. Muck is a rich, highly organic type of soil that serves as a growth medium for most vegetation in the Florida Everglades. Because muck can be destroyed by a variety of natural causes (e.g. fire, erosion, etc), knowledge of mean muck depth is important in the management of the Everglades. In order to develop a management plan for the Everglades, researchers expect to sample various locations throughout the area. Since production of muck depends on many factors they intend to subdivide the Everglades region into eight subareas, each one based on a distinct vegetation type (eg. a subregion for grassesinterlaced with streams, another subregion for woody bushes on hummocks, etc). Within each subarea a random sample of mud cores will be taken. Sampling will be done by taking a soil core and observing the depth at which the soil changes from muck to some other type. 6. What variable is being analyzed by the scientists? a. amount of muck b. surface vegetation c. destruction of muck d. depth of muck By definition, a variable is the kind of information measured or observed on the observational unit. So, since they are measuring the depth of muck that is the variable under analysis. 7. The population of interest is a. the entire set of measurements that could be taken anywhere in the Everglades b. the total amount of muck in the Everglades c. the set of all measurements taken at sampling locations d. the mean muck depth in the Everglades The population is, by definition, the set of all possible measurements or values on the units of interest. Here, that means that the population is the set of all possible measurements that could be taken in the Everglades. Why the other possibilities are incorrect: Total amount of muck is a characteristic or parameter of the population (total = mean depth x area), so that isn’t correct; the set of measurements at sampling locations is the sample not the population; and, the mean muck depth is the parameter or population characteristic to be estimated as stated in the problem description. 8. This type of sampling design is called a stratified sampling design. Question 9. In a study of the
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