A survey claims that 8 out of 10 doctors recommend aspirin for their patients wi

Question

A survey claims that 8 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.80, a random sample of 100 doctors' results in 75 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to? Explain why a Type I error and a Type II error have an inverse relationship. A Type II error is committed if we make: a. a correct decision when the null hypothesis is false. b. a correct decision when the null hypothesis is true. c. an incorrect decision when the null hypothesis is false. d. an incorrect decision when the null hypothesis is true.

Explanation / Answer

proportion p = 75/100 = 0.75

standard error = sqrt( p * (1-p))/n

= sqrt( 0.75 *0.25 / 100)

= 0.0433

test static = p - p-hat/standard error

= 0.75 - 0.8/0.0433

= -1.1547

a type I error is reject H0 when it is actually true

a type II error is accept Ho when it is actually false

as it can been seen that , they inverse relationship

choose c)

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