Question

Elementary Statistics (7th edition)

Chapter 8

review question 7

For Exercises 1 through 20, perform each of the following steps.

1. State the hypotheses and identify the claim.
2. Find the critical value(s).
3. Compute the test value.
4. Make the decision.
5. Summarize the results

7. Weights of Men’s Soccer Shoes Is lighter better? A random sample of men’s soccer shoes from an inter-national catalog had the following weights (in ounces).

10.8	9.8	8.8	9.6	9.9
10	8.4	9.6	10	9.4
9.8	9.4	9.8

At α=0.05, can it be concluded that the average weight is less than 10 ounces? Assume the variable is normally distributed.

Answer 1

The mean for the sample data is calculated as

and standard deviation as

s= 0.585

Since the sample size=13 <30 and Population standard deviation is not gien hence t- distribution is applicable for Hypothesis testing now,

a) The Hypotheses are:

b) Rejection Region:

Reject Ho if T < -t _{0.05, 12}= -1.78 , where 12 is the degree of freedom calculated using n-1

c) Test statistic:

P-value:

P-value computed using T statistic calculated above is computed using excel tool as

0.01<P-value<0.025

d) Decision and result:

Since T < -t and P-value < 0.05 hence we rekect the null hypothesis and conclude that there is enough evidence to support the claim that mean is less than 10 ounces.