Question

A hospital director is told that 79% of the treated patients are insured. The director wants to test the claim that the percentage of insured patients is less than the expected percentage. A sample of 340 patients found that 255 were insured. At the 0.10 level is there enough evidence to support the director's claim? Answer 2 Points Tables Keypad Keyboard Shortcuts > There is sufficient evidence to support the claim that the percentage of insured patients is less than 79%. There is not sufficient evidence to support the claim that the percentage of insured patients is less than 79% Prev Next

Answer 1

Ans a) There is sufficient evidence to support the claim that the percentage of the insured patient is less than 79%

Explanation:

Null Hypothesis:

Alternate Hypothesis states that the percentage of insured patients is less than the expected percentage

Sample proportion: $\hat{p} = \frac{x}{n} = \frac{255}{340} = 0.75$

Test statistics:

$z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$= \frac{0.75-0.79}{\sqrt{\frac{0.79(1-0.79)}{340}}}$

Test statistics z = -1.81

P-value = 0.0351 /* we can find p-value using excel function: =NORM.S.DIST(-1.81,TRUE) */

Since P-value < 0.1 (we reject null Hypothesis)

Conclusion:There is sufficient evidence to support the claim that the percentage of the insured patient is less than 79%