Question

Question: A cloth manufacturing company claims that the mean tearing strength of their
curtain fabric is 120 pounds. A government inspection agency conducted tests on 49 curtain
lengths revealing a mean strength of 115 pounds with a standard deviation of 20 pounds. At the
10% level of significance, does the governments’ information show that the mean tearing
strength of the fabric is lower than manufacturer’s claim?

Answer 1

Answer)

Null hypothesis Ho : u = 120

Alternate hypothesis Ha : u < 120

As the population standard deviation is unknown here

We will use t distribution table to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (115 - 120)/(20/√49) = -1.75

Degrees of freedom is = n-1 = 48

For 48 dof and -1.75 test statistics

P-value from t distribution table is = 0.043254

As the obtained p-value is less than the given significance 0.1

We reject the null hypothesis Ho

We have enough evidence to conclude that the mean tearing
strength of the fabric is lower than manufacturer’s claim