Question

Blood samples from 10 persons were sent to each of two labs for cholesterol determination. The measurements are recorded below:
Table 1. Serum Cholesterol measurements of Lab 1 and Lab 2
Subject Lab 1 Lab 2
1 296 318
2 268 287
3 244 260
4 272 279
5 240 245
6 244 249
7 282 294
8 254 271
9 244 262
10 262 285

Is there a statistical significant difference (at α = 0.01) in the cholesterol level reports by lab 1 and lab 2? Perform the following steps:

a. State in symbolic form the null and alternative hypothesis
b. Should you use the independent t test or the paired t test to answer this question?
c. Once you choose the appropriate t test, state:
a. α
b. degrees of freedom (df)
c. Critical value
d. Calculate the t test statistic
e. Provide the exact p-value
f. Calculate 99% C.I. and interpret the confidence interval using one or two sentences.
g. State your conclusion (reject or fail to reject the null hypothesis)
h. Express your conclusion in less technical terms (“there is or there is not a significant difference……..”)
i. Based on your conclusion state what type of error you might have made (Type I or Type II error).