Question

A semiconductor manufacturer produces drivers that are used in the electrical system of vehicles. The customer requires that the number of controls is not more than 0.05, and the manufacturer demonstrates these characteristics of the manufacturing process with this quality level, specifying a significance level of 5%. To verify this, the semiconductor manufacturer takes a random sample of 200 devices and finds that only 4 of them are defective. Verify with the 5% significance level that the manufacturer can meet the customer with the required quality. Verbally describe how to reach the solution mentioning the statistical concepts, as well as, justify the statistic and sample distribution to use and then write the procedure that must be clean and ordered

Answer 1

Solution :

Given that ,

n = 200

x = 4

The null and alternative hypothesis is

H0 : p = 0.05

Ha : p < 0.05

This is the left tailed test .

= x / n = 4 / 200 = 0.02

P0 = 0.05

1 - P0 = 1 - 0.05 = 0.95

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.02 - 0.05 / [0.05( 1 - 0.05 ) / 200 ]

= -1.947

The test statistic -1.947