ESS210B
Prof. Jin-Yi Yu
Example
qA
manufacturer of sports equipment has developed a new fishing line that he claims
has a mean breaking strength of 8 kilograms with a standard deviation of 0.5
kilogram. Test the hypothesis that m = 8
kilograms against the alternative that m ¹ 8 kilograms if a random sample of 50 lines is
tested and found to have a mean breaking strength of 7.8 kilogram. Use a
0.01 level of significance.
Answer:
1. a = 0.01
2.
H0: m = 8
kilograms
H1: m ¹ 8
kilograms
3.
Use Z statistics (because sample mean has a normal distribution)
4.
Critical region: Z-a/2 < -2.58 and Za/2 > 2.58
5.
Z = (7.8-8)/0.5/(50)0.5 = -2.828 < Z-a/2
6. Reject H0 and conclude that the average breaking strength is not equal to 8
but, in fact, less than 8
kilograms.
