Question

A hospital director is told that 30% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is less than

the expected percentage. A sample of 340 patients found that 85 were uninsured. State the null and alternative hypotheses.

Answer 1

Answer:
`H_0: p=0.30`

`H_a: p <0.30`

Explanation:

Definition:

Null Hypothesis : It is a statement about the population parameter that contains = , ≤ and ≥ signs.

Alternative hypothesis : It is also a statement about the population parameter against the null hypothesis that contains ≠ , < and > signs.

For the given situation.

Let
`\mu` be the population proportion of treated patients are uninsured.

A hospital director is told that 30% of the treated patients are uninsured.

Then, Null Hypothesis :
`H_0: p=0.30`

The director wants to test the claim that the percentage of uninsured patients is less than the expected percentage.

i.e. Alternative hypothesis :
`H_a: p <0.30`

Hence, the set of hypothesis :

`H_0: p=0.30`

`H_a: p <0.30`