Question

Assume that a simple random sample has been selected from a normally distributed population. We want to test the claim that for the population of female college students at a particular university, the mean weight is given by µ=132lb. The sample data are summarized as follow: n=20, x=137lb, and s=14.2 lb. Use a significant level of α=0.1.

a. Identify the relevant variable and parameter

b. State null and alternative hypothesis

c. Find the test statistic value

d. Find and interpret the P-value and interpret the conclusion

e. Is there a probability of making type II error (Yes or No).

Answer 1

a.)
n = 20

b) The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.
c) Now, the value of test static can be found out by following formula:

d) Using Excel's function =, the P-value for in an t-test with 19 degrees of freedom can be computed as .
Since P = 0.1318 > 0.1, we fail to reject the null hypothesis
e) Since we failed to reject the null hypothesis, yes there is a probability of making type 2 error.
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