## Answers

*ANSWER:*

*Given that,*

**5)**

null hypothesis : Assume that there is no association between adverse reaction and new drug

alternative hypothesis : Assume there is an association between these two variables.

**How to calculate the chi-square statistic by hand.** First we have to calculate the expected value of the two nominal variables. We can calculate the expected value of the two nominal variables by using this formula:

Where

= expected value

= Sum of the i_{th} column

= Sum of the k_{th} row

N = total number

After calculating the expected value, we will apply the following formula to calculate the value of the Chi-Square test of Independence:

= Chi-Square test of Independence

= Observed value of two nominal variables

= Expected value of two nominal variables

Degree of freedom is calculated by using the following formula:

DF = (r-1)(c-1)

Where

DF = Degree of freedom

r = number of rows

c = number of columns

here r = c = 2

**Expected values are :**

E_{11} = (84*18) / 182 = 8.308

E_{12} = (18*98) / 182 = 9.692

E_{21} = (164*84) / 182 = 75.692

E_{22} = (164*98) / 182 = 88.308

**Decision:**

then ^{2} = 1.798(observed)

tabulated ^{2}_{0.05 ; 1} = 3.841

**observed ^{2} < tabulated ^{2}**

**We failed to reject the null hypothesis . According to the given data the two variables are independent.**

**Conclusion:**

*it is concluded that null hypothesis Ho is not rejected.Therefore there is NOT enough evidence to claim that two variables are depedent at the 0.05 significance level.*