A new drug to treat psoriasis has been developed and is in clinical testing. Assume that those individuals given the drug are examined before receiving the treatment and then again after receiving the treatment to determine if there was a change in their symptom status. If the initial results showed that 2.0% of individuals entered the study in remission, 77.0% of individuals entered the study with mild symptoms, 16.0% of individuals entered the study with moderate symptoms, and 5.0% entered the study with severe symptoms calculate and interpret a chi-squared test to determine if the drug was effective treating psoriasis given the information below from the final examination.

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.

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