# Stats-Assignments:Answer the following questions covering materials from previous chapters in your textbook. Each question is worth 3.5 points.

**Note: **Assignment one, Assignment two, Assignment three, and Assignment four

Each is 20 total 100

**Assignment One**

Instructions | |

This quiz will cover the material from Chapters 1–5 (Modules One, Two, and Three) in Basic Biostatistics: Statistics for Public Health Practice. The quiz will focus on solving and analyzing problems. |

Answer the following questions covering materials from previous chapters in your textbook. Each question is worth 3.5 points.

1. Prospective studies on nutrition often require subjects to keep detailed daily dietary logs. In contrast, retrospective studies often rely on recall. Which method (dietary logs or retrospective recall) do you believe is more likely to achieve accurate results? Explain your response.

2. We often have a choice of whether to record a given variable on either a quantitative or a categorical scale. How does one measure age quantitatively? Provide an example by which age can be measured categorically.

3. Telephone surveys may use a telephone directory to identify individuals for study. Speculate on the type of household that would be undercovered by using this sampling frame.

4. Could the number “0000” appear in a table of random digits? If so, how likely is this?

5. Body weights of 18 diabetics expressed as a percentage of ideal (defined as body weight divided by ideal body weight x 100) are listed: {107, 119, 99, 114, 120, 104, 88, 114, 124, 116, 101, 121, 152, 100, 125, 114, 95, 117}. Construct a stem-and-leaf plot of these data and interpret your findings.

6. Name three measures of central location.

7. To assess the air quality in a surgical suite, the presence of colony-forming spores per cubic meter of air is measured on three successive days. The results are as follows: {12, 24, 30}. Calculate the mean and standard deviation for these data.

8. In a lottery game, a person must select 5 numbers from a total of 40. Tracy has chosen 7, 8, 9, 10, 11. Jaime has chosen 39, 17, 37, 5, 28. Who has a greater chance of winning?

9. In a box, there are 8 orange, 7 blue, and 6 red balls. One ball is selected randomly. What is the probability that it is neither orange nor red?

10. A __________ is a numerical quantity that takes on different values depending on chance. There are two types of random variables. __________ form a countable set of possible values. __________ form an unbroken continuum of possible values.

**Assignment Two**

Instructions | |

This quiz will cover material from Chapters 6–9 (Modules Three and Four) in Basic Biostatistics: Statistics for Public Health Practice. |

Answer the following questions covering materials from previous chapters in your textbook. Each question is worth 3.5 points.

1. A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 15% of the time. In eight attempts, what is the probability of achieving exactly two successful calls?

2. The prevalence of a trait is 76.8%.

a. In a simple random sample of *n* = 5, how many individuals are expected to exhibit this characteristic?

b. How many would you expect to see with this characteristic in a simple random sample of *n* = 10?

c. What is the probability of seeing nine or more individuals with this characteristic in a simple random sample of *n* = 10?

3. Linda hears a story on National Public Radio stating that one in six eggs in the United States are contaminated with *Salmonella*. If *Salmonella*contamination occurs independently within and between egg cartons and Linda makes a three egg omelet, what is the probability that her omelet will contain at least one *Salmonella* contaminated egg?

4. Suppose that heights of 10-year old boys vary according to a Normal distribution with µ = 138 cm and σ = 7 cm.

a. What proportion of this population is less than 150 cm tall?

b. What proportion is less than 140 cm in height?

c. What proportion is between 150 and 140 cm?

5. The Wechsler Adult Intelligence Scale scores are calibrated to vary according to a normal distribution with µ = 100 and σ = 15. What Wechsler scores cover the middle 50% of the population? In other words, identify the 25th percentile and 75th percentile of the population.

6. Suppose that scores on the biological sciences section of the Medical College Admissions Test (MCAT) are normally distributed with a mean of 9.2 and a standard deviation of 2.2. Successful applicants to become medical students had a mean score of 10.8 on this portion of the test. What percentage of applicants had a score of 10.8 or greater?

7. A survey selects a simple random sample of *n* = 500 people from a town of 55,000. The sample shows a mean of 2.30 health problems per person (standard deviation = 1.65). Based on this information, say whether each of the following statements is *true* or *false*. Explain your reasoning in each instance.

a. The standard deviation of the sample mean is 0.074.

b. It is reasonable to assume that the number of health problems per person will vary according to a normal distribution.

c. It is reasonable to assume that the sampling distribution of the mean will vary according to a normal distribution.

8. Ten people are given a choice of two treatments. Let *p* represent the proportion of patients in the patient population who prefer treatment A. Among the 10 patients asked, 7 preferred method A. Assuming there is no preference in the patient population (i.e., *p* = 0.5), calculate P(*X* > 7).

9. A simple random sample of 18 male students at a university has an average height of 70 inches. The average height of men in the general population is 69 inches. Assume that male height is approximately normally distributed with σ = 2.8 inches. Conduct a two-sided hypothesis test to determine whether the male students have heights that are significantly different than expected. Show all hypothesis testing steps.

10. True or false? The *p*-value refers to the probability of the data or data more extreme assuming the null hypothesis.

**Assignment Three**

Instructions | |

This is an opportunity to demonstrate your understanding of the concepts practiced in Chapters 11 and 12. |

Answer the following questions covering materials from previous chapters in your textbook. Each question is worth 3.5 points.

1. A sample of 49 sudden infant death syndrome (SIDS) cases had a mean birth weight of 2998 g. Based on other births in the county, we will assume σ = 800 g. Calculate the 95% confidence interval for the mean birth weight of SIDS cases in the county. Interpret your results.

2. A vaccine manufacturer analyzes a batch of product to check its titer. Immunologic analyses are imperfect, and repeated measurements on the same batch are expected to yield slightly different titers. Assume titer measurements vary according to a normal distribution with mean µ and σ = 0.070. Three measurements demonstrate titers of 7.40, 7.36 and 7.45. Calculate a 95% confidence interval for true concentration of the sample.

3. True or false? A confidence interval for µ is 13 + 5.

a. The value 5 in this expression is the estimate’s standard error.

b. The value 13 in this expression is the estimate’s margin of error.

c. The value 5 in this expression is the estimate’s margin of error.

4. The term *critical value* is often used to refer to the value of a test statistic that determines statistical significance at some fixed α level for a test. For example, +1.96 are the critical values for a two-tailed *z*-test at α = 0.05. In performing a *t*-test based on 21 observations, what are the critical values for a one-tailed test when α = 0.05? That is, what values of the *t*stat will give a one-sided *p*-value that is less than or equal to 0.05? What are the critical values for a two-tailed test at α = 0.05?

5. When do you use a *t*-procedure instead of a *z*-procedure to help infer a mean?

6. A simple random sample of *n* = 26 boys between the ages of 13 and 14 has a mean height of 63.8 inches with a standard deviation 3.1 inches. Calculate a 95% confidence interval for the mean height of the population.

7. Identify whether the studies described here are based on (1) single samples, (2) paired samples, or (3) independent samples.

a. An investigator compares vaccination histories in 30 autistic schoolchildren to a simple random sample of non-autistic children from the same school district.

b. Cardiovascular disease risk factors are compared in husbands and wives.

c. A nutritional exam in applied to a random sample of individuals. Results are compared to expected means and proportions.

8. We wish to detect a mean difference of 0.25 for a variable that has a standard deviation of 0.67. How large a sample is needed to detect the mean differences with 90% power at α = 0.05 (two-sided)?

9. Identify two graphical methods that can be used to compare quantitative data from two independent groups.

10. A questionnaire measures an index of risk-taking behavior in respondents. Scores are standardized so that 100 represents the population average. The questionnaire is applied to a sample of teenage boys and girls. The data for boys is {72, 73, 86, 95, 95, 95, 96, 97, 99, 125}. The data for girls is {89, 92, 93, 98, 105, 106, 110, 126, 127, 130}. Explore the group differences with side-by-side boxplots.

**Assignment Four**

Instructions | |

Complete a very short quiz covering the main topics in this course. |

Answer the following questions covering materials from previous chapters in your textbook. Each question is worth 7 points.

1. A trial evaluated the fever-inducing effects of three substances. Study subjects were adults seen in an emergency room with diagnoses of the flu and body temperatures between 100.0 and 100.9ºF. The three treatments (aspirin, ibuprofen and acetaminophen) were assigned randomly to study subjects. Body temperatures were reevaluated 2 hours after administration of treatments. The below table lists the data.

Table: Decreases in body temperature (degrees Fahrenheit)

Group 1 (aspirin) | 0.95 | 1.48 | 1.33 | 1.28 | ||

Group 2 (ibuprofen) | 0.39 | 0.44 | 1.31 | 2.48 | 1.39 | |

Group 3 (acetaminophen) | 0.19 | 1.02 | 0.07 | 0.01 | 0.62 | -0.39 |

Complete an ANOVA for the above. What do you conclude?

2. Evidence of nonrandom differences in group means occurs when the variance between groups is __________ the variance within groups.

3. Why are scatterplots necessary when investigating the relationship between quantitative variables?

4. *r* is always greater than or equal to _____ and less than or equal to _____. Perfect negative association is present when *r* = _____. Perfect positive association is present when *r* = _____. Between *r* = -0.56 and *r* = +0.46, the stronger correlation is _____.

5. Besides linearity, what conditions are needed to infer population slope β (3 more conditions)? Besides linearity, what conditions are needed to infer population correlation coefficient ρ (2 more conditions)?