Question

Prompt 1: Provide an example, real or imagined, and describe under what circumstances a hypothesis test for the difference between two means or two proportions can be conducted. Include what significance level should be used based on the seriousness of a Type I error for your test; and identify possible confounding variables that may skew the results.

Answer 1

Prompt-1

Suppose, a researcher desires to investigate whether eating sea salt raises blood pressure more than eating normal table salt. He randomly selects two groups, first with 13 people and second with 15 people. He assigns Group 1 on a high sea salt diet for 2 weeks whereas Group 2 on a high table salt diet. He measures their blood pressure after 2 weeks. The mean systolic blood pressure for Group 1 is found to be 126 with a sample standard deviation of 4.0, while for Group 2 the mean is found to be 116 with a sample standard deviation of 3.7.

This test is based on two different groups and we have to analyze whether mean of group 1 is significantly higher than that of group 2 or not. As encountering type I error suggests that eating sea salt raises blood pressure more than eating normal table salt, it would be serious to commit such error whenever it does not happen at all. So we have to take significance level as 0.10 or 0.05.

A possible confounding variable is difference between mean natural blood pressure of these two groups of people. If there is a significant difference in mean blood pressure between these two groups without any treatment as sea salt and table salt, then this will affect our experiment and very often our conclusion may be also faulty.

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