(Chapter 8) Question # 1: In this study, two independent, random samples with in
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(Chapter 8) Question # 1: In this study, two independent, random samples with interval/ratio data were collected. In Group 1, a random sample of 133 primary hypertension (PH) patients were taken and each person's total cholesterol (measured in mg/dl) was recorded. In Group 2, a random sample of 41 normotensive (NT) was taken and their total cholesterol was recorded. Data are given in Table below. Use 5-step hypothesis testing process to check if the PH group's population average total cholesterol level is significantly higher than 210 mg/dl. Use alpha = 5%. (20 points). Data Column Population Variance (o?) PH NT 879.47 Sample Mean (X) 214.71 193.20 133 41 1091.96Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 210
Alternative hypothesis: u > 210
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 18.6177
DF = n - 1
D.F = 132
t = (x - u) / SE
t = 1.83
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 1.83.
Thus the P-value in this analysis is 0.035.
Interpret results. Since the P-value (0.035) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that average total cholestrol level is significantly higher than 210 mg/dl.
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