Question

A manufacturer of sports equipment has developed a new synthetic fishing line that the company claims has a mean breaking strength of 8 kg with a standard deviation of 0.5 kg. To test the claim, a random sample of 50 lines is tested and found to have a mean breaking strength of (7.8 kg) and a standard deviation of (0.7 kg). Could you conclude that the manufacturer claim justified at 0.01 level of significance?( state any assumptions made)   

Subject: Probability and statistics

Answer 1

Step 1:

H0: = 8

Ha: 8

Null hypothesis states that the mean breaking strength of new synthetic fishing line is 8.

Step 2 : test statsitics

n = 50

sample mean = =  7.8

population sd = = 0.5

Assuming that the data is normally distributed. Also as the population sd is given we will use z stat.

Step 3:

level of significane = 0.01

The z-critical values for a two-tailed test, for a significance level of α=0.01

zc = −2.58 and zc = 2.58

As the z stat ( -2.828) falls in the rejection area, we reject the Null hypothesis.

Hence the manufactures claim that mean breaking strength of new synthetic fishing line is 8 is not justified at 0.01 level of significance.