Question

The Berkl fishing tackle company is interested in seeing the effects of sunlight on the strength of its premier fishing line. According to specifications the average breaking strength of a particular line is 10 pounds.

a) What would be the null and alternative hypothesis for testing whether sunlight decreased the average breaking strength of the fishing line to below 10 pounds?

b) Calculate the P-Value if a sample of 21 segments of fishing line that had been exposed to large amounts of sunlight had a sample average breaking strength of 9.67 pounds with a standard deviation of 1.1 pounds.

c) What conclusion would you make at an alpha level of .05? (State your conclusion in terms of the problem)

Answer 1

Solution :

a) The null and alternative hypothesis is ,

H₀ :   = 10

H_a : < 10

Test statistic = z

= ( - ) / s / n

= (9.67- 10) / 1.1 / 21

= -1.37

This is the left tailed test,  

b) degrees of freedom = n - 1 = 21 - 1 = 20

P(t < -1.37)

P-value = 0.0929

c) = 0.05  

P-value >

fail to reject the null hypothesis .