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 against using a random sample of specimens. Calculate the P-value if the observed statistic is . Suppose that the distribution of the sample mean is approximately normal.

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.

0.02275

Step-by-step 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)

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2