Question

A certain manufactured product is supposed to contain 23% potassium by weight. A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2. If the mean percentage is found to differ from 23, the manufacturing process will be recalibrated.

The null and alternate hypotheses are H0 : μ = 23 versus H1 : μ 6= 23.

Compute the P-value.

Answer 1

: Mean percentage of potassium by weight

Two tailed test:

Given,

Number of specimens in the sample :sample size : n=10

Sample average percentage : = 23.2

Sample standard deviation :s =0.2

Hypothesized mean : = 23

Degrees of freedom = n-1=10-1=9

For two tailed test :

For 9 degrees of freedom , P(t>3.1646) = 0.00573

P-value = 0.01146