Question

A manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8 kilograms. If a random sample of 20 lines is tested and found to have a sample mean breaking strength of 7.8 kilograms with a sample variance of 0.25. By using hypothesis testing, does this suggest at a 0:01 level of significant that the mean breaking strength is not 8 kilograms? Assume the population of the breaking strength to be normal.

Answer 1

H0:Null Hypothesis: = 8 ( mean breaking strength of a new synthetic fishing line is 8 kilograms ) (Claim)

HA: Alternative Hypothesis: 8 ( mean breaking strength of a new synthetic fishing line is not 8 kilograms )

n = Sample Size = 20

= Sample Mean = 7.8

s = Sample SD = = 0.50

= 0.01

df = 20 - 1 = 19

From Table, critical values of t = 2.861

Test Statistic is given by:

Since calculated value of t = - 1.789 is greater than critical value of t = - 2.861, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data support the claim that mean breaking strength of a new synthetic fishing line is 8 kilograms .