Suppose we plan to conduct a study to see this is true that students gain weight as freshmen.a) Describe a study design that would require a matched- pairs t procedure to analyze the results.&nbsp;b) Describe a study design that would require a two- sample t procedure to analyze the results.

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Suppose we plan to conduct a study to see this is true that students gain weight as freshmen.a) Describe a study design that would require a matched- pairs t procedure to analyze the results.&amp;nbsp;b) Describe a study design that would require a two- sample t procedure to analyze the results.

Velsenw · Accepted Answer

Step 1 We require to test the hypothesis that students gain weight in the first year of their college. Part a: In the first situation, paired t-test will be used when we consider a random sample of students from a college or university, at the beginning of their first year and keep a data of their weights. This will be our first sample. Then after the completion of their first year again measure the weights of the same students. This will be our second sample. Now we can test whether there is an increase in their average weight or their weights remain same. Since we have collected the data from same students after waiting for a year, we will use paired t-test here. So basic conditions for using paired t-test are: 1. The underlying population should be normally distributed. 2. The two samples are of equal sizes. 3. The two samples are not independent, but the observations are pared together (xi,yi) say, corresponding to the same ith sample unit. Under the null hypothesis µµH0:µ1=µ2 the test statistic is t=d―Sn∼tn−1where,di=xi−yi,i=1,2,…,n S=1/(n−1)[∑d2−((∑d)2)/n] Step 2 Part b: In the second situation independent sample t-test is used when two sample are independently collected. Collect a random sample of weights of students at beginning of their first year. Another, sample of weights of students who joined their second year can be collected. And the average weight from the two samples can be compared using independent sample t-test. Conditions for using the two independent sample t-test. 1. Two underlying populations must be normally distributed. 2. Sample sizes may be equal or unequal. 3. The two samples are independent of each other. Under the null hypothesis µµH0:µ1=µ2 the test statistic is t=(x―−y―)S1n1+1n2∼tn1+n2−2 S=1/n1+n2−2[∑xi−x¯2+∑yi−y¯2]

Many people believe that students gain weight as freshmen. Suppose we plan to conduct a study to see if this is true. a) Describe a study design that

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