Question

A prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of active ingredient. The manufacturer periodically collects data to determine if the production process is working properly. A random sample of 64 pills has a mean of 250 ppm with a standard deviation of 12 ppm. Let µ denote the average amount of the active ingredient in pills of this allergy medicine. The null and alternative hypotheses are Ho: µ = 245, Ha: µ ≠ 245. The level of significance is 1%. The T-test statistic is 3.33 with a P-value of 0.0014. What is the correct conclusion?

Answer 1

Solution :

Given that,

=  245

= 250

s = 12

n = 64

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   =  245

H_a :     245

Test statistic = t

= ( - ) / s / n

= (250 - 245 ) / 12 / 64

= 3.333

Test statistic t value = 3.333

P-value = 0.0014

= 0.01

P-value <

0.0014 < 0.01

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 245, at the 0.01 significance level.