Question

(PLEASE TYPE THE ANSWERS)(STATISTICS 500)

instructions : describe a research study in your area of study Introduction: Description of the study including the purpose and importance of the research question being asked. What is your null hypothesis? What is your research or alternative hypothesis?

Participants/Sampling Method: Describe the sample collected for the study, as well as the sampling method. How were your participants selected? Who is your population of interest? If you did a survey, how many will you survey to ensure your target sample size? How did you come up with that number? What do you expect your response rate to be? What was your sample size? How representative is the sample of the population under study? Procedures: How were the data collected? Was a survey or questionnaire used to collect data? What are the independent and dependent variables? How are the variables defined and measured? Are the variables nominal, ordinal, interval, or ratio measurement scales? Are the data collected in a way that avoids bias? What is your selected alpha level?

Data Analysis: What statistical test was used to analyze the data? Describe the statistical test. What are the requirements? Did you meet those requirements? Describe why your selected method was appropriate to answer your research question. Make up a test statistic value. Given that value, do you reject or fail to reject the null hypothesis? Is your p < .05 or p > .05 (assuming alpha = .05)? Results & Discussion: Did your analysis answer your research question? Explain. What are the practical implications of your results?

Answer 1

Answers: Description of the study -- We wanted to see if, in a particular college, the habit of smoking is independent of the gender of students, in order to start a smoking awareness program. The null and the alternative hypotheses for this study are:

H0: Smoking is independent of gender and Ha: Smoking is not independent of gender.

Our population of interest is entire college students. We collect a random sample of 50 students from each year and ask them whether or not they smoke. Here smoking habit and gender both are nominal variables. Since the students are selected randomly we can ensure that bias is negligible. The selected level of significance is 0.05.

We use the Chi-square test for independence to test and analyze the hypotheses. This test can be used when the two assumptions are made, which are, i) The two variables should be measured in a nominal or ordinal scale and ii) The two variables should consist of two or more (categorical), independent groups. Here the requirements are met.

The data is given in a 2x2 contingency table in the attached images below.

The test statistic is T = sum_(i=1(1)r)sum_(j=1(1)c) (O_i,j - E_i,j)² / E_i,j where r and c are the number of rows and columns and O_i,j and E_i,j are the observed and expected values of the variables.

Here the value of the test statistic is T(observed) = 1.9732

The p-value associated with the test statistic is = 0.1601

We know that we reject our null hypothesis if p-value < the level of significance, otherwise fail to reject it. So, since here p-value > 0.05, we fail to reject the null hypothesis and conclude on the basis of the obtained sample, at a 5% level of significance that smoking habit is independent of gender.

(The solutions are obtained from R-software. Code and output images are attached below.)