Question

We want to compare the serum cholesterol levels of recent immigrants with the levels found in the general population of the US. It is known that the mean cholesterol level for a certain age group in the US is 189 mg/dL. A random sample of 100 recent immigrants of the same age group finds a mean of 180 mg/dL. Assume that a population standard deviation is 49. Test at the 5% level to see if the level for recent immigrants is different. Give the null and alternate hypotheses. Decide if you accept or reject the null hypothesis

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 189

H_a :    189

Test statistic = z =

= ( - ) / / n

= (180 - 189) / 49 / 100

Test statistic = z = -1.84

P(Z < -1.84) = 0.0329

P-value = 2 * P(Z < -1.84)

P-value = 2 * 0.0329

P-value = 0.0658

= 0.05  

P-value >

Fail to reject the null hypothesis .