Sample Final Exam
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Drexel University *
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Course
411
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
3
Uploaded by BarristerMusic4065
Math 410 Sample Final Exam Answer each of the following questions in a clear and concise manner. For each problem, include all details of the calculations and R scripts. 1.
Answer the following questions based on a population of mosquito fish with a known mean length of 35.29 mm and a standard deviation of 4.59 mm. a.
What is the probability that any individual sampled at random from this population would have a length of 43 mm or larger. b.
What is the probability that a random sample of twelve individuals have a mean length of 43 mm or larger. c.
What is the probability that any individual sample at random would have a length between 33 mm and 43 mm? 2.
Use the data from Digital Appendix I and several procedures from your statistical software to see if the lengths of bluegill sunfish tends to follow a normal distribution. a.
Construct a histogram. Describe its shape using correct terms you previously learned. Is the histogram symmetric and bell shaped? b.
Create a quantile plot and describe the shape of the curve. Does it look linear? c.
Determine the values of skewness and kurtosis. What are the values expected for a normal distribution? Are your computed values close to the expectation? d.
Finally, run a Shapiro-Wilk normality test. e.
What do you conclude –
does this sample of bluegill sunfish lengths follow a normal distribution? 3.
According to the National Center for Health Statistics for 2012, 24% of adults in Missouri smoke. You wish to know the probability of selecting a random sample of 50 people containing 20 or fewer smokers from this population. a.
Use a statistical program to determine the exact probability of getting 20 or fewer smokers. b.
Now use the normal approximation of the binomial distribution to answer the same question. Compare your answers. Are they similar? 4.
The northern leopard frog which is easily distinguished from other frogs by the spots covering its body, is common throughout the United States and Canada. The burnsi morph of the leopard frog is caused by a mutation in a single gene a
nd is characterized by a lack of spots on the frog’s back. In a sample of 450 frogs in Minnesota, 15% of the frogs were of the burnsi morph. Calculate the 95% confidence interval for this proportion and interpret the result. 5.
A CO
2
level in a sample of 62 kitchens with gas cooking appliances was monitored during a one-
week period. The sample mean CO
2
level in ppm was 645.16 and the sample standard deviation was 154.43. Compute the 90% confidence interval for the population mean. 6.
The label on a company’s
energy drinks claims that they contain an average caffeine concentration of 260 mg/oz. The mean caffeine concentration of 16 randomly sampled drinks was 269, with a standard deviation of 13.1. Are the drink labels accurate?
7.
The FDA has established that the concentration of a certain pesticide in apples may not exceed 10 ppb. A random sample of 120 apples from a major orchard had an average pesticide content of 10.04 ppb with a standard deviation of 0.16 ppb. Are the apples within the FDA requirement? 8.
The wattle thickness (in millimeters) of 15 randomly selected chickens was measured before and after treatment with phytohemagglutinin (PHA). Does treatment with PHA increase wattle thickness? Chicken Number Pre-treatment Post-treatment 1 1.05 3.48 2 1.01 5.02 3 0.78 5.37 4 0.98 5.45 5 0.81 5.37 6 0.95 3.92 7 1.00 6.54 8 0.83 3.42 9 0.78 3.72 10 1.05 3.25 11 1.04 3.66 12 1.03 3.12 13 0.95 4.22 14 1.46 2.53 15 0.78 4.39 9.
A study was conducted to test whether human social interactions increase in response to obtaining the common flu vaccine. The number of people encountered 36 hours before immunization was compared to the number of people encountered 36 hours after immunization for 12 individuals. Does the vaccine increase the encounter rate? Prior studies indicated that similar data fail the assumptions for parametric tests. Individual ID Before Immunization After Immunization 1 90 94 2 59 100 3 56 85 4 72 84 5 66 106 6 56 91 7 61 60 8 44 112 9 58 127 10 68 67 11 66 125 12 81 108
10.
Fourteen subjects were given an experimental drug and asked if their sense of well-being improved, became worse, or did not change after taking the drug. We wish to know if the drug is effective in improving one’s sense of well
-being. The results were as followed. a.
6 reported an improvement b.
3 reported no change c.
5 reported feeling worse
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