Question

A special engineered bridge cable has a breading strength of 6000 lbs. A researcher selects a

sample of 25 of these cables and find an average breaking strength is 5956 lbs with a

standard deviation of 138 lbs. Assuming the variable is normally distributed, is there enough

evidence to claim that the breaking strength is less than 6000 lbs at 0.10 significance level

a. State the hypotheses and identify the claim.

b. Compute the test value.

c. Find the p-value.

d. Make the decision to reject or not reject the null hypothesis

e. Summarize the results

Answer 1

n = 25

S = 138

a)

claim : breaking strength is less than 6000 lbs

Null and alternative hypothesis is

H0 : u = 6000

H1 : u < 6000

Level of significance = 0.10

b)

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

c)

Degrees of freedom = n - 1 = 25-1=24

P-value = 0.062 ( using t table)

d)

P-value , Reject H0

e)

conclusion : At level of significance ,There is sufficient evidence to conclude that the breaking strength is less than 6000 lbs