Provide one example each of a study where you will use a one-sample hypothesis test and one for a two-sample test. Justify your choice of test; that is, why did you choose a one-sample or two-sample test
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Example of a one-sample hypothesis test:
A nutritionist wants to determine if a new weight loss program is effective in reducing body weight. The nutritionist selects a random sample of 50 individuals who participate in the program for 3 months. The null hypothesis is that the weight loss program has no effect on body weight (population mean weight change is zero). The alternative hypothesis is that the weight loss program leads to a decrease in body weight (population mean weight change is less than zero). In this case, a one-sample hypothesis test can be used as only one group (participants in the weight loss program) is being compared to a known population mean (zero weight change).
Example of a two-sample hypothesis test:
A pharmaceutical company wants to determine if a new drug is more effective in reducing blood pressure compared to an existing drug. They randomly assign a group of individuals to take the new drug and another group to take the existing drug. After 8 weeks of treatment, blood pressure measurements are recorded for both groups. The null hypothesis is that the new drug is not more effective than the existing drug (population mean blood pressure reduction is equal in both groups). The alternative hypothesis is that the new drug leads to greater blood pressure reduction than the existing drug (population mean blood pressure reduction is higher in the new drug group). In this case, a two-sample hypothesis test can be used as two independent groups (participants taking the new drug and participants taking the existing drug) are being compared to each other.
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