Complete 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 xbar = 11.5. Suppose that the distribution of the sample mean is approximately normal.
Answer:
0.02275
Explanation:
Given :
Population mean μ = 12
Standard deviation, σ = 0.5
Sample size, n = 4
Observed statistic, xbar = 11.5
H0 : μ = 12
H1 : μ < 12
The test statistic = (xbar - μ) ÷ σ/sqrt(n)
Test statistic =. (11.5 - 12) ÷ 0.5/sqrt(4)
Test statistic = - 0.5 ÷ 0.5/2
Teat statistic = - 0.5 / 0.25 = - 2
Since, it is stated that, distribution is approximately normal ; then we can use the Z distribution and obtain our Pvalue.
We could obtain P value using the Pvalue Z distribution calculator at α = 0.05, 1 - tail
Pvalue = 0.02275
Or
P(x < - 2) = 0.02275 (Z distribution table)