Question

A hospital director is told that 60% of the treated patients are insured. The director wants...

A hospital director is told that 60% of the treated patients are insured. The director wants to test the claim that the percentage of insured patients is below the expected percentage. A sample of 160 patients found that 80 were insured. Find the value of the test statistic. Round your answer to two decimal places.

Math   Statistics-And-Probability   
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Answer #1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p =0.60

Ha : p 0.60

n = 160

x =80

= x / n = 80 / 160 =0.50

P0 = 0.60

1 - P0 = 1 -0.60 =0.40

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.50-0.60 / [(0.60*0.40) / 160]

= -2.58

Test statistic = z =-2.58

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