Question

****Return to problem 5.3.2 and answer the questions posed, using the t distribution rather than the standard normal distribution.  In other words, the problem was originally posed assuming that the population’s standard deviation σ is known.  Now answer the questions assuming the standard deviation is estimated from the sample itself.  What are the degrees of freedom?***

5.3.2 The study cited in Exercise 5.3.1 reported an estimated mean serum cholesterol level of 183 for women aged 20–29 years. The estimated standard deviation was approximately 37. Use these estimates as the mean m and standard deviation s for the U.S. population. If a simple random sample of size 60 is drawn from this population, find the probability that the sample mean serum cholesterol level will be:

(a) Between 170 and 195 (b) Below 175 (c) Greater than 190

The real question is bolded the other is just the info needed to answer the question.

Answer 1

Solution:

The degrees of freedom is

(a) Between 170 and 195

Answer: We have to find

Using the t-score formula, we have:

Now using the t distribution table, we have:

(b) Below 175

We have to find

Using the t-score formula, we have:

   

Now using the t distribution table, we have:

(c) Greater than 190

We have to find

Using the t-score formula, we have:

   

Now using the t distribution table, we have: