Question

An experiment was conducted for better understanding of the effectiveness of a particular type of drug for reducing bad cholesterol (LDL) level. The purpose of the experiment was to determine whether different dosages used have significant different outcomes in average LDL reduction. Twenty subjects with LDL at around 250 to 300 mg/dL had participated in the study and were randomly divided into four groups. Each group was given a specific level of dosage of the drug each day for one month, with a control group that only provided with placebo. The reduction in LDL was recorded and showed in the following table. Positive number indicates reduction and negative numbers indicates increasing in DLD. Use statistical software to analyze the data and answer the following question.

Control	Light Dosage Level	Medium Dosage Level	Heavy Dosage Level
7	25	73	81
−3	17	60	71
6	22	55	79
5	21	41	60
15	12	36	85

Perform a One-way ANOVA test to see if there is significant difference between the outcomes from the four treatment groups, at 5% level of significance, by answering the following questions.

1. Perform nonparametric Kruskal Wallis test and conclude the analysis using the p-value of the test.

Null hypothesis:

Alternative hypothesis:

Report p-value and use it to draw the conclusion:

[Paste software output here!]

Answer 1

The first image is the output of one way ANOVA, in which we found the test statistic F = 51.436 and the P-value is 0.00001, which is less than the level of significance alpha 0.05 therefore we reject the null hypothesis and concluded that the mean of four treatment groups are highly statistically significant.

The second image is the Output of Kruskall Wallis test.

The hypothesis of the test are

Null hypothesis H0: The mean of four treatment groups are not statistically significant.

Alternate hypothesis Ha: The mean of four treatment groups are statistically significant.

We found the test Statistc H = 16.94 and the P-value of the test is 0.00073 which is less than the level of significance alpha 0.05, therefore we reject the null hypothesis and concluded that the mean of four treatment groups are statistically significant.