Question

A horseshoe for horseshoe pitching should not weigh less than 2.625 pounds. In a sample of 28 horseshoes. the average weight is 2.48 pounds with a sample standard deviation of 0.3 pounds. We wish to test H0: mu equals 2.625 against HA: mu space less than space 2.625 at alpha space equals space 0.05. You may assume the distribution of weights is approximately normal.

a) Are the hypotheses being tested right-tailed, left-tailed, or two-tailed?

b) Determine the value of the test statistic from the given data. Show your work for partial credit.

c) Determine the critical value (or p-value) for this test.

d) What do you conclude about the average weight of the population of horseshoes?

Answer 1

Solution:

a)

This is a left-tailed test.

b)

The test statistics,

t =( - )/ (s /n)

= ( 2.48 - 2.625 ) / ( 0.3 / 28 )

= -2.558

c)

Critical value of  the significance level is α = 0.05, and the critical value for a left-tailed test is

= -1.703

d)

Since it is observed that t = -2.558 < = -1.703, it is then concluded that the null hypothesis is rejected.

There is sufficient evidence to claim that the horseshoe for horseshoe pitching should not weigh less than 2.625 pounds.