Question

A hospital director believes that over 42% of the test tubes contain errors and feels an audit is required. A sample of 450 reports found 216 errors. Is there sufficient evidence at the 0.05 level to substantiate the hospital director's claim?

State the null and alternative hypotheses for the above scenario.

solve all steps please

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.42

Ha : p > 0.42

= x / n = 216 / 450 = 0.480

P0 = 42% = 0.42

1 - P0 = 1 - 0.42 = 0.58

Test statistic = z

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

= 0.48 - 0.42 / [0.42 (0.58) / 450 ]

= 2.579

P(z > 2.579) = 1 - P(z < 2.579) = 1 - 0.995 = 0.005

P-value = 0.005

= 0.05    

0.005 < 0.05

P-value <

Reject the null hypothesis .