Hypothesis Tests for Two Samples

  Independent Samples
            One of our researchers wishes to determine whether people with high blood pressure can reduce their systolic blood pressure by taking a new drug we have developed. The sample data is shown below, where  represents the mean blood pressure of the treatment group and  represents the mean for the control group. Use a significance level of 0.01 and the critical value method to test the claim that the drug reduces the blood pressure. We do not know the values of the population standard deviations.

	Treatment Group				Control Group
	n1		80		n2		70
			186.7				201.9
	s1		38.5		s2		39.8

1.      Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.

Answer and Explanation

 

1: r your step-by-step This is a left-tailed test. This is because we are trying to determine whether people with high blood pressure can reduce their systolic blood pressure by taking a new drug. So, the alternative hypothesis takes a ‘less than’ sign.

2  2.       Calculate the critical value and the test statistic.

 

3.       Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.

Answer and Explanation

 

Dependent samples

This same new drug was tested on another group, but this time the test was done before the drug was administered, and then tested after the drug was given to the same group. The results are shown in the table below:

Subject	Before	After
1	200	191
2	174	170
3	198	177
4	170	167
5	179	159
6	182	151
7	193	176
8	209	183
9	185	159
10	155	145
11	169	146
12	210	177

Use the data above with a significance level of 0.05 to test the claim that for the populations of blood pressures before and after the drug, the differences have a mean greater than 0 mm Hg (so the claim is that the drug helps lower the blood pressure). Use the P-Value method to determine whether or not to reject the null hypothesis and state your conclusion.

4.       Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.

Answer and Explanation

5.       Calculate the test statistic and the P-Value.

Answer and Explanation

We find the differences between the before and after values and denote the differences by d. Then calculate the mean and standard deviation of before, after and the difference. Subject Before After Difference 1 200 191 9 2 174 170 4 3 198 177 21 4 170 167 3 5 179 159 20 6 182 151 31 7 193 176 17 8 209 183 26 9 185 159 26 10 155 145 10 11 169 146 23 12 210 177 33 Mean 185.3333 166.75 18.58333 Standard Deviation 17.06849 14.86378 10.10363 We assume that the differences are normally distributed. We use the test statistic  P(t<6.3714) is obtained from a statistical software or calculator. The P-value of 6.3714 at 11 degrees of freedom and 0.05 is 0.00002 (Soper, 2017)

6.       Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.

Answer and Explanation

Since P<α, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the new drug lowers high blood pressure.

References

Soper, D. (2017, December 1). Free Statistics Calculators. Retrieved from Free Statistics Calculator: https://www.danielsoper.com/statcalc/default.aspx