Question

We are focused on Independent Samples in this chapter. When answering please label the steps 1-5. I have looked for this answer on other parts of chegg but the question states in bold Assume equal variances. Thank you so much in advance! I've tried this question and gotten it wrong so I seriously appreciate the help.

A hypertension trial is mounted and 12 participants are randomly assigned to receive either a new treatment or a placebo. Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment. The data are as follows.

Placebo	New Treatment
134	114
143	117
148	121
142	124
150	122
160	128

Is there a difference in mean SBP between treatments? Assume equal variances. Run the test at a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available.

Answer 1

(1)

H0:Null Hypothesis: (There is no significant difference in mean SBP between treatments)

HA:Alternative Hypothesis: (There is significant difference in mean SBP between treatments)

(2) The appropriate test:

2 Independent Samples t - test with equal variances

(3) Degrees of Freedom = n1 + n2 - 2 = 12 - 2 = 10

= 0.05

From Table, critical values of t = 2.2281

Decision Rule: Reject null hypothesis if t < - 2.2281 OR t > 2.2281

(4)

From the given data, the following statistics are calculated:

n1 = 6

1 = 146.16667

s1 = 8.7731

n2 = 6

2 = 121

s2 = 4.9800

Test statistic is:

t = (146.1667 - 121)/4.1184 = 25.1667/4.1184 = 6.1108

So,

Test statistic is:

t = 6.1108

(5) Since the calculated value of t = 6.1108 is greater than critical value of t = 2.2281, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that there is significant difference in mean SBP between treatments