Examples of Different Study Designs with Practice Questions

Prove that the reduced row echelon forms of the matrices$\left(\begin{array}{cccccccc}1& 1& 4& 8& 0& -1& -1& \\ 1& 2& 3& 9& 0& -5& -2\\ 0& -2& 2& -2& 1& 14& 3\\ 1& 4& 1& 11& 0& -13& -4\end{array}\right)\left(\begin{array}{ccccc}0& -3& 3& 1& 5\\ 0& 1& -1& 0& 0\\ 0& 2& -2& 0& -3\end{array}\right)$

are the two matrices. 

The point of the reduced row echelon form is that the corresponding system of linear equations is in a particularly simple form, from which the solutions to the system $AX=Cin(4)$ can be determined immediately.

 

The pathogen Phytophthora capsici causes bell pepper plants to wilt and die. A research project was designated to study the effort of soil water content and the spread of the disease in fields of bell peppers. It is thought that too much water helps spread the disease. The fields were divided into rows and quadrants. The soil water content (percent of water by volume of soil) was determined for each plot. An important first step in such a research is to give a statistical description of the data.

1. A drug is being tested in a chronic disease whose condition waxes and wanes over time. Which of the following study designs is most effective in evaluating the efficacy and safety of a new therapy
for this disease?
A. Retrospective Cohort
B. Case-Control
C. Prospective, Randomized, Active Control, Parallel Group Design
D. Prospective, Randomized, Active Control, Crossover Design

The American Journal of Political Science (Apr. 2014) published a study on a womans

Use either the critical-value approach or the P-value approach to perform the required hypothesis test. Approximately 450,000 vasectomies are performed each year in the United States. In this surgical procedure for contraception, the tube carrying sperm from the testicles is cut and tied. Several studies have been conducted to analyze the relationship between vasectomies and prostate cancer. The results of one such study by E. Giovannucci et al. appeared in the paper “A Retrospective Cohort Study of Vasectomy and Prostate Cancer in U.S. Men” (Journal of the American Medical Association, Vol. 269(7), pp. 878-882). Of 21,300 men who had not had a vasectomy, 69 were found to have prostate cancer, of 22,000 men who had had a vasectomy, 113 were found to have prostate cancer. a. At the 1% significance level, do the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer? b. Is this study a designed experiment or an observational study? Explain your answer. c. In view of your answers to parts (a) and (b), could you reasonably conclude that having a vasectomy causes an increased risk of prostate cancer? Explain your answer.

Determine whether the study depicts an observational study or an experimental study.
A study was done to see if sugar consumption can cause hypoeractivity in children. The researcher took four groups of children and assigned different amounts of sugar the children had to consume. After a certain period of​ time, they assessed whether or not the children were hyperactive.

When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 90% confident that the population proportion is estimated to within 0.05? (Round your answer up to the nearest whole number.)

In Exercises, state whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.
Starting Salaries. The National Association of Colleges and Employers (NACE) compiles information on salary offers to new college graduates and publishes the results in Salary Survey.

The article “Anodic Fenton Treatment of Treflan MTF” describes a two-factor experiment designed to study the sorption of the herbicide trifluralin. The factors are the initial trifluralin concentration and the \(\displaystyle{F}{e}^{{{2}}}\ :\ {H}_{{{2}}}\ {O}_{{{2}}}\) delivery ratio. There were three replications for each treatment. The results presented in the following table are consistent with the means and standard deviations reported in the article. \(\begin{array}{|c|c|}\hline \text{Initial Concentration (M)} & \text{Delivery Ratio} & \text{Sorption (%)} \\ \hline 15 & 1:0 & 10.90 \quad 8.47 \quad 12.43 \\ \hline 15 & 1:1 & 3.33 \quad 2.40 \quad 2.67 \\ \hline 15 & 1:5 & 0.79 \quad 0.76 \quad 0.84 \\ \hline 15 & 1:10 & 0.54 \quad 0.69 \quad 0.57 \\ \hline 40 & 1:0 & 6.84 \quad 7.68 \quad 6.79 \\ \hline 40 & 1:1 & 1.72 \quad 1.55 \quad 1.82 \\ \hline 40 & 1:5 & 0.68 \quad 0.83 \quad 0.89 \\ \hline 40 & 1:10 & 0.58 \quad 1.13 \quad 1.28 \\ \hline 100 & 1:0 & 6.61 \quad 6.66 \quad 7.43 \\ \hline 100 & 1:1 & 1.25 \quad 1.46 \quad 1.49 \\ \hline 100 & 1:5 & 1.17 \quad 1.27 \quad 1.16 \\ \hline 100 & 1:10 & 0.93 \quad 0.67 \quad 0.80\\ \hline \end{array}\) a) Estimate all main effects and interactions. b) Construct an ANOVA table. You may give ranges for the P-values. c) Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.

Is the gift you purchased for that special someone really appreciated? This was the question investigated in the Journal of Experimental Social Psychology (Vol. 45, 2009). Toe researchers examined the link between engagement ring price (dollars) and level of appreciation of the recipient ${\displaystyle (\text{measured on a 7-point scale where}1=\text{"not at all" and}7=\text{to a great extent"}).}$ Participants for the study were those who used a popular Web site for engaged couples. The Web site's directory was searched for those with "average" American names (e.g., "John Smith," "Sara Jones"). These individuals were then invited to participate in an online survey in exchange for a $10 gift certificate. Of the respondents, those who paid really high or really low prices for the ring were excluded, leaving a sample size of 33 respondents.a) Identify the experimental units for this study.b) What are the variables of interest? Are they quantitative or qualitative in nature?c) Describe the population of interest.d) Do you believe the sample of 33 respondents is representative of the population? Explain. e. In a second, designed study, the researchers investigated whether the link between gift price and level of appreciation was stronger for birthday gift givers than for birthday gift receivers. Toe participants were randomly assigned to play the role of gift-giver or gift-receiver. Assume that the sample consists of 50 individuals. Use a random number generator to randomly assign 25 individuals to play the gift-receiver role and 25 to play the gift-giver role.

When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.05? (Round your answer up to the nearest whole number.)

The article “Rocker Shoe Put to the Test: Can it Really Walk the Walk as a Way to Get in Shape?” (USA TODAY, October 12, 2009) describes claims made by Skechers about Shape-Ups, a shoe line introduced in 2009. These curved-sole sneakers are supposed to help you “get into shape without going to the gym” according to a Skechers advertisement. Briefly describe how you might design a study to investigate this claim. Include how you would select subjects and what variables you would measure. Is the study you designed an observational study or an experiment?

Use either the critical-value approach or the P-value approach to perform the required hypothesis test. For several years, evidence had been mounting that folic acid reduces major birth defects. A. Czeizel and I. Dudas of the National Institute of Hygiene in Budapest directed a study that provided the strongest evidence to date. Their results were published in the paper “Prevention of the First Occurrence of Neural-Tube Defects by Periconceptional Vitamin Supplementation” (New England Journal of Medicine, Vol. 327(26), p. 1832). For the study, the doctors enrolled women prior to conception and divided them randomly into two groups. One group, consisting of 2701 women, took daily multivitamins containing 0.8 mg of folic acid, the other group, consisting of 2052 women, received only trace elements. Major birth defects occurred in 35 cases when the women took folic acid and in 47 cases when the women did not. a. At the 1% significance level, do the data provide sufficient evidence to conclude that women who take folic acid are at lesser risk of having children with major birth defects? b. Is this study a designed experiment or an observational study? Explain your answer. c. In view of your answers to parts (a) and (b), could you reasonably conclude that taking folic acid causes a reduction in major birth defects? Explain your answer.

Response rates to Web surveys are typically low, partially due to users starting but not finishing the survey. The factors that influence response rates were investigated in Survey Methodology (Dec. 2013). In a designed study, Web users were directed to participate in one of several surveys with different formats. For example, one format utilized a welcome screen witb a white background, and another format utilized a welcome screen with a red background. The "break-off rates," i.e., the proportion of sampled users who break off the survey before completing all questions, for the two formats are provided in the table.

$\begin{array}{|ccc|}\hline & \text{White Welcome Screen}& \text{Red Welcome Screen}\\ \text{Number of Web users}& 190& 183\\ \text{Number who break off survey}& 49& 37\\ \text{Break-off rate}& 0.258& 0.202\\ \hline\end{array}$

a) Verify the values of the break-off rates shown in the table.

b) The researchers theorize that the true break-off rate for Web users of the red welcome screen will be lower than the corresponding break-off Tate for users of the white welcome screen. Give the null and alternative hypotbesis for testing this theory.

c) Conduct the test, part b, at ${\displaystyle \alpha =0.10.}$ What do you conclude?

In a similar study using the same design (sample of $n=9$ participants), the individuals who wore the shirt produced an average estimate of $M=6.4$ with $SS=162$.
The average number who said they noticed was (population mean) 3.1. Calculate a One Sample t-test using a two-tailed test with ${\displaystyle \alpha =.05}$.

The pathogen Phytophthora capsici causes bell pepper plants to wilt and die. A research project was designed to study the effect of soil water content and the spread of the disease in fields of bell peppers. It is thought that too much water helps spread the disease. The fields were divided into rows and quadrants. The soil water content (percent of water by volume of soil) was determined for each plot. An important first step in such a research project is to give a statistical description of the data. Soil Water Content for Bell Pepper Study $$\begin{array}{cccccccccccccc}15& 14& 14& 14& 13& 12& 11& 11& 11& 11& 10& 11& 13& 16\\ 9& 15& 12& 9& 10& 7& 14& 13& 14& 8& 9& 8& 11& 13\\ 15& 12& 9& 10& 9& 9& 16& 16& 12& 10& 11& 11& 12& 15\\ 10& 10& 10& 11& 9\end{array}$$ If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation.

In an experiment designed to study the effects of illumination level on task performance (“Performance of Complex Tasks Under Different Levels of Illumination,” J. Illuminating Eng., 1976: 235–242), subjects were required to insert a fine-tipped probe into the eyeholes of ten needles in rapid succession both for a low light level with a black background and a higher level with a white background. Each data value is the time (sec) required to complete the task.
$\begin{array}{|cccccccccc|}\hline Subject& (1)& (2)& (3)& (4)& (5)& (6)& (7)& (8)& (9)\\ Black& 25.85& 28.84& 32.05& 25.74& 20.89& 41.05& 25.01& 24.96& 27.47\\ White& 18.28& 20.84& 22.96& 19.68& 19.509& 24.98& 16.61& 16.07& 24.59\\ \hline\end{array}$
Does the data indicate that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time? Test the appropriate hypotheses using the P-value approach.