Example: assume that cholesterol levels in us women aged 21-40 are normally distributed with mean 190 mg/dl and standard deviation 40 mg/dl. it is unknown whether cholesterol levels among recent asian immigrants are higher or lower than those in the general us population. blood tests are performed on 200 female asian immigrants aged 21-40; the mean level was found to be 181.52 mg/dl. the standard deviation for female asian immigrants is known to be 40 mg/dl. the the null hypothesis that the mean for asian women is the same as the mean for us women in general (190 mg/dl). use a significance value of 5%. h0 : ha : α= critical value(s): test statistic: conclusion:

We reject   H₀

We have evidence, to conclude that the mean of cholesterol level in asian inmigrants is not the same as it is in US women

Step-by-step explanation:

Test hypothesis

1. Hypothesis  H₀     ⇒  null hypothesis         μ₀ = 190

                           alternative hypothesis         μₐ  ≠ 190

We see a two tail test at significant value of 5 % with sample of n = 200

α  = 0.05    we look for a two tails test the  α/2   =  0.025

from z table:

z(c) = + 1.96     on the right       and    z(c)  =  -  1.96   on the left

Now for z (s) = ( z - μ₀ )/ ( σ/√n)   ⇒ (181,52 - 190) / (40/√200)

z(s) = - ( 8,48* 14,14)/40     z(s) = - 119,91/40        z(s) = -  2.99

z(s) < z(c)       - 2.99  <  - 1.96

Then z(s) is in the rejection zone we reject   H₀