State your hypotheses Which hypothesis test should you use S

State your hypotheses. Which hypothesis test should you use? Stale your rejection rule (use the p-valuc approach) Show how the test statistic was calculated (write down the formula and plug in the What is ihe p-value? State your conclusion.

Solution

Given    n = 374     x = 15   p = x/n = 15/374 = 0.0401   q = 1-p = 1- 0.0401 = 0.9599

P=2/100 = 0.02    Q = 1-P = 1- 0.02 = 0.98

The null hypothesis is

H₀ :   P = 0.02 i.e., to examine the spam received is equal to 2%

Against the alternative hypothesis

H₁ : P > 0.02 i.e., to examine the spam received is greater than 2%

Here we use two tailed test to test the hypothesis

The test statistic is

Z = ( (p - P)/(PQ)/n ) N(0,1)

Z = ((0.0401 - 0.02)/(0.02)(0.98)/374

Z_cal   =   2.7765

Here   Z _tab value   at 0.01 level of significance is 2.58

Therefore Z_cal is less than Z_tab we accept the null hypothesis

The p   - value is   0.003

conclusion : the spam received is equal to 2%