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?

null and alternative hypothesis? sigma? z or t distribution? critical value to fourth decimal place. test statical value is? =, p value? p value significance level? is the test insignificant or significant?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 120
Alternative Hypothesis, Ha: μ < 120

t distribtiom

Rejection Region
This is left tailed test, for α = 0.1 and df = 48
Critical value of t is -1.2994.
Hence reject H0 if t < -1.2994

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (115 - 120)/(20/sqrt(49))
t = -1.75

P-value Approach
P-value = 0.0433
As P-value < 0.1, reject the null hypothesis.

The results are significant