Question

A hospital director believes that above 24% of the lab reports contain errors and feels an audit is required. A sample of 150 reports found 48 errors. Is there sufficient evidence at the 0.10 level to substantiate the hospital director's claim?

State the null and alternative hypotheses for the above scenario.

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**Answer:**

Since the hospital director believes above 24% of the lab reports conatin errors. (>24%). This is a right-tailed test

The null and alternative hypothesis are

**Null** -
**H _{0}**: p = 0.24

**Alternative** -
H_{a} : p > 0.24

= 48 / 150 = 0.32

Test statistics

z = - po / Sqrt(po(1-po)/n)

= 0.32 - 0.24 / Sqrt(0.24 * 0.76 / 150)

= 0.08 / 0.0349

= 2.294

Rejection region to reject H0 is test statistics > 1.645 for zcrit for 90% (LOS)

=> **we have
sufficient evidence to reject H0.**

We conclude that at 0.1 level, we have enough evidence to
**support the claim
that above 24% of the lab reports contain errors and feels an audit
is required.**

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