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In: Statistics and Probability

To test Upper H 0: pequals0.60 versus Upper H 1: pless than0.60, a simple random sample...

To test Upper H 0: pequals0.60 versus Upper H 1: pless than0.60, a simple random sample of nequals450 individuals is obtained and xequals252 successes are observed. (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the alphaequals0.05 level of significance, compute the probability of making a Type II error, beta, if the true population proportion is 0.56. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.50.

Expert Solution

The null and alternative hypothesis are defined as,

a)

“A Type II error is the probability of failing to reject the null hypothesis when the null hypothesis is actually FALSE. Type II error is denoted by . While the value can be defined as probability of rejecting the null hypothesis when the null hypothesis is False also called power of the test.

b)

The true population is,

The probability of type II error is given by,

The probability is obtained by calculating the z score for proportion,

The probability is obtained from standard normal distribution table for z = 1.7094 (in excel use function =1-=NORM.S.DIST(1.7094,TRUE))

Power

c)

If, true population proportion is,

The probability of type II error is given by,

The probability is obtained by calculating the z score for proportion,

The probability is obtained from standard normal distribution table for z = 1.7094 (in excel use function =1-=NORM.S.DIST(4.2426,TRUE))

Power

orchestra answered 2 years ago

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