Question

 

The sample data is shown below, where x1 represents the mean blood pressure of the treatment group and x2 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

x ?_1     186.7 x ?_2     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.

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 1

Solution:-

1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_treatment> u_Control
Alternative hypothesis: u_treatment < u_Control

Note that these hypotheses constitute a one-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 6.4154
DF = 148

t = [ (x₁ - x₂) - d ] / SE

t = - 2.37

t_critical = - 2.35

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

2)

Interpret results. Since the t-value (- 2.37) is less than the critical value (- 2.35), we have to reject the null hypothesis.

3)

Interpret results. Since the P-value (0.0095) is less than the significance level (0.01), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the drug reduces the blood pressure.