Question

A manufacturer of electric lamps is testing a new production method that will be considered acceptable if the lamps produced by this method result in a normal population with an average life of 2,400 hours and a standard deviation equal to 300. A sample of 100 lamps produced by this method has an average life of 2,320 hours. Can the hypothesis of validity for the new manufacturing process be accepted with a risk equal to or less than 5%?

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 2400

H_a : < 2400

= 2320

= 2400

= 300

n = 100

Test statistic = z

= ( - ) / / n

= (2320 - 2400) / 300 / 100

= -2.67

Test statistic = -2.67

P(z < -2.67) = 0.0038

P-value = 0.0038

= 0.05

P-value <

Reject the null hypothesis .

Validity for the new manufacturing process be accepted with a risk equal to or less than 5% .