Question

A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0:μ=12 against H1:μ<12 using a random sample of n=4 specimens. Calculate the P-value if the observed statistic is x¯=11.5. Round your final answer to five decimal places (e.g. 98.76543).

Answer 1

Answer:

P-value = 0.02275

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =  12 kilograms

Sample mean, $\bar{x}$ = 11.5 kilograms

Sample size, n = 4

Alpha, α = 0.05

Population standard deviation, σ = 0.5 kilograms

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 12\\H_A: \mu < 12$

We use one-tailed(left) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{11.5 - 12}{\frac{0.5}{\sqrt{4}} } = -2$

We calculate the p-value from the standard z-table:

P-value = 0.02275