Question

Assume the accuracy a manufactured device follows normal distribution ?(?, ?2) . According to the requirements, the standard deviation shouldn't be more than 0.9. But 19 devices were taken for assessment and found that the standard deviation is 1.2. Is the standard deviation acceptable at the level ? = 0.05 ?

Answer 1

Where we want to test the hypothesis as

Ho :

H1 :

Provided information

n = 19 , , S = 1.2

Test statistic = (n-1) * (S^2) / ()

Test statistic =( 18 *1.2^2)/ ( 0.9 )

Test statistic = 32.00

DF = n- 1 = 18

P- value = p ( chi square < 32.00)

P-value = 0.978

Decision : Do not reject Ho, because p-value is greater than 0.05

Conclusion : There is not enough evidence to support the claim that standard deviation acceptable ( ) at the level ? = 0.05

Thank you!