A manufacture of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8kg with standard deviation of 0.5kgs.Test the hypothesis that the mean greater than 8kgs.If random sample of 49 liners is tested and found to have mean breaking strength of 8.2kgs.Use the 0.05 level of significance

Question

A manufacture of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8kg with standard deviation of 0.5kgs.Test the hypothesis that the mean greater than 8kgs.If random sample of 49 liners is tested and found to have mean breaking strength of 8.2kgs.Use the 0.05 level of significance

Answer 1

H0: μ = 8kg

H1: μ > 8kg

α = 0.05

n = 49

x̅ = 8.2kg

σ = 0.5kg

Calculate the test statistic:

z = (x̅ - μ) / (σ/√n)

z = (8.2 - 8) / (0.5/√49)

z = 0.4/0.1

z = 4

Look up the critical value in the z-table for α = 0.05. The critical value is 1.645.

Since the test statistic (4) is greater than the critical value (1.645), we reject the null hypothesis and conclude that the mean breaking strength is greater than 8kg.