Question

In this preliminary study at a level of significance of α-001 wa below 185 on the average? The deviation is, s 26.3. Assume the data is normally 5) after e mean cholesterol after the study is x=1689 and the standard a (3 pts) what type of test will you conduct? In order to test if the total cholesterol has been lowe red to below 185 after 6 months state the null and alternative hypotheses. (6 pts) Calculate the t statistic for the test, round to 3 decimal places. How many degrees of freedom? b) (4 pts) Using the attached table determine the p-value for the test and at a level of significance of a 0.01 what is your conclusion? c) d) (7 pts) Make a 99% confidence interval of the population mean of the cholesterol level after taking the drug for 6 months. Round to 2 decimal places.

Answer 1

a)

One sided t test

H0; mu = 185
Ha: mu < 185

b)

test statistics;

t = (xbar -mu)/(s/sqrt(n)))
= ( 168.9 - 185)/(26.3/sqrt(6))
= -1.499

df = 6 -1 = 5

c)

p value = P(t < -1.499)

P value = 0.0970

Fail to reject H0 as p value > 0.01

d)

The t value at 99% confidence interval is,

alpha = 1 - 0.99 = 0.01
alpha/2 = 0.01/2 = 0.005
t(alpha/2,df) = t(0.005,5) = 4.032

Margin of error = E =z *(s/sqrt(n))
= 4.032 *(26.3/sqrt(6))
= 43.2913

CI = mean +/- E
= 168.9+/- 43.2913
= (125.61 , 212.19)

The 99% CI is (125.61 , 212.19)