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 190 mg/dL. A random sample of 100 recent immigrants of the same age group finds a mean of 181.52 mg/dL. Assume that a population standard deviation is 48.23. 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 :   = 190

H_a :    190

Test statistic = z

= ( - ) / / n

= (181.2 - 190) / 48.23 / 100

Test statistic = z = -1.82

P (Z < -1.82) = 0.0344

P-value = 2 * P (Z < -1.82)

P-value = 2 * 0.0344

P-value = 0.0688

= 0.05  

P-value >

Fail to reject the null hypothesis .