Question

p-value problem. Suppose the director of manufacturing at a clothing factory needs to determine wheteher a new machine is producing a particulcar type of cloth according to the manufacturer s specification which indicate that the cloth should have mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds. THe p value for this hypothesis testing scenario is

Answer 1

The P-Value is 0.07186

Explanation:

GIven that :

Mean = 70

standard deviation = 3.5

sample size n = 49

sample mean = 69.1

The null hypothesis and the alternative hypothesis can be computed as follows;

`H_o : \mu = 70 \\ \\ H_1 : \mu \\eq 70`

The standard z score formula can be expressed as follows;

`\mathtt{z = (\overline X - \mu)/((\sigma)/(√(n)))}`

`\mathtt{z = (69.1 - 70)/((3.5)/(√(49)))}`

`\mathtt{z = (-0.9)/((3.5)/(7))}`

z = -1.8

Since the test is two tailed and using the Level of significance = 0.05

P- value = 2 × P( Z< - 1.8)

From normal tables

P- value = 2 × (0.03593)

The P-Value is 0.07186