Question

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. Historical data reveal a standard deviation of 0.18 mg, based upon years of production records. A random sample of 24 bulbs has a mean of 3.62 mg of mercury. If we give the benefit of the doubt to GreenBeam: (a) test whether or not we should believe the manufacturer’s claim. Use a 1% significance level. (b) Find the p-value for this test. ( I understand A just need "part b")

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   3.50

H_a : > 3.50

= 3.62

= 3.50

s = 0.18

n = 24.

Df = n - 1 = 24 - 1 = 23

Test statistic = t

= ( - ) / s / n

= (3.62 - 3.50) / 0.18 / 24

= 3.27

Test statistic = 3.27

Using t table,

P-value = 0.0017