Answer:
Step-by-step explanation:
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: The distribution of severity of psoriasis cases at the end and prior are same.
Alternative hypothesis: The distribution of severity of psoriasis cases at the end and prior are different.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.
Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
DF = k - 1 = 4 - 1
D.F = 3
(Ei) = n * pi
Category observed Num expected num [(Or,c -Er,c)²/Er,c]
Remission 380 20 6480
Mild
symptoms 520 770 81.16883117
Moderate
symptoms 95 160 24.40625
Severe
symptom 5 50 40.5
Sum 1000 1000 6628.075081
Χ2 = Σ [ (Oi - Ei)2 / Ei ]
Χ2 = 6628.08
Χ2Critical = 7.81
where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, Ei is the expected frequency count for level i, Oi is the observed frequency count for level i, and Χ2 is the chi-square test statistic.
The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 6628.08.
We use the Chi-Square Distribution Calculator to find P(Χ2 > 19.58) =less than 0.000001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.
We reject H0, because 6628.08 is greater than 7.81. We have statistically significant evidence at alpha equals to 0.05 level to show that distribution of severity of psoriasis cases at the end of the clinical trial for the sample is different from the distribution of the severity of psoriasis cases prior to the administration of the drug suggesting the drug is effective.
