# Hypothesis Testing Question

Teacher's questions

### Hypothesis Testing Question

Question:
Records kept at a hospital show that 3 out of every 10 patients who come to A&E have to wait more than an hour before seeing a doctor.
The hospital decides to increase staffing in the A&E to reduce the proportion.
It was found that out of the next 20 patients 2 had to wait more than an hour.
Test at the 5% level of significance whether the new staffing has decreased the number of patients waiting over an hour.
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### Re: Hypothesis Testing Question

This is a problem with sample proportions. The proportion of patients who wait more than one hours drops from 3/10 to 2/20= 1/10 and your sample has size 20. That can be approximated by the standard normal distribution with $$z= \frac{0.1- 0.3}{\sqrt{\frac{0.3(1- 0.3)}{200}}}$$

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