Question

A hospital director is told that 80% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 340 patients found that 255 were insured. At the 0.02 level, is there enough evidence to support the director's claim?

Answer 1

Given that, n = 340 and x = 255

sample proportion = 255/340 = 0.75

significance level = 0.02

The null and the alternative hypotheses are,

H₀ : p = 0.80

H_a : p < 0.80

Test statistic is,

since, it is left-tailed test,

p-value = P(Z < -2.30) = 0.0107

=> p-value = 0.0107

Since, p-value = 0.0107 < significance level = 0.02

We reject the null hypothesis ( H₀ ).

Conclusion: There is sufficient evidence to support the  claim that the percentage of insured patients is under the expected percentage. (i.e. less than 80%).