Question

a hospital director is told that 54% of the treated patients are insured. The director wants to test the claim that the percentage of patients is below the expected percentage. A sample of 380 patients found that 190 were insured. At the 0.01 level, is there enough evidence to support the directors claim?

Step 5 of 7: Identify the level of significance.

Answer 1

Solution:

Step 5 of 7: Identify the level of significance.

Answer : 0.01

Full solution is as

The null and alternative hypothesis ,

H₀: p = 0.54

H_a: p < 0.54

Left tailed test

Let   be the sample proportion.

  = x/n = 190/380= 0.5

The test statistic z is

z =  

=  (0.5 - 0.54)/[0.54*(1 - 0.54)/380]

= -1.56

Test statistic z = -1.56

Now , for left tailed test

p value = P(Z < -1.56) = 0.0594

p value is 0.0594

p value is greater than the given level of significance 0.01

Fail to reject H₀

There is not sufficient evidence to to support the directors claim.