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The Bureau of Labor Statistics (BLS) reported that 9.9% of adults aged 20 to 24 years were unemployed in February 2015. Suppose that Jacqui believes that in her city the unemployment rate is higher than the reported proportion. She determines the unemployment status of 450450 randomly selected adults in the given age range. She decides to conduct a

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Answer #1

Hypotheses are:

: P 0.099

Ha : p > 0.099

Standard deviation of the proportion is:

V/p(1-2-v00999 i p (1-p) 0.099 (1-0.099) 0.099) = 0.0141 450

The critical value of z for which we will reject the null hypothesis is 1.645. The critical value of sample proportion for which we will reject the null hypothesis is

p-0.099 0.0141 p-p

0.099 0.0141 1.645_ P 0.099

p-0.122 1945 0.122

Standard deviation of the proportion for p= 0.110 is:

V/pil-P)-v0.1 101 4 0 0.110) = 0.0147 /p (1-p) /0.110(1-0.110) 450

The z-score for and p = 0.110 is

p~ 0.122

0.82 0.0147

The power of the test is

power = P(z > 0.82) = 1 - P(z <= 0.82) = 0.2061

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• The Bureau of Labor Statistics (BLS) reported that 9.9% of adults aged 20 to 24 years...

  The Bureau of Labor Statistics (BLS) reported that 9.9% of adults aged 20 to 24 years were unemployed in February 2015. Suppose that Jacqui believes that in her city the unemployment rate is higher than the reported proportion. She determines the unemployment status of 450 randomly selected adults in the given age range. She decides to conduct a z-test for the proportion p of unemployed adults in her town aged 20 to 24 years old. Determine the power to reject...

Answer 1

Hypotheses are:

: P 0.099

Ha : p > 0.099

Standard deviation of the proportion is:

V/p(1-2-v00999 i p (1-p) 0.099 (1-0.099) 0.099) = 0.0141 450

The critical value of z for which we will reject the null hypothesis is 1.645. The critical value of sample proportion for which we will reject the null hypothesis is

p-0.099 0.0141 p-p

0.099 0.0141 1.645_ P 0.099

p-0.122 1945 0.122

Standard deviation of the proportion for p= 0.110 is:

V/pil-P)-v0.1 101 4 0 0.110) = 0.0147 /p (1-p) /0.110(1-0.110) 450

The z-score for and p = 0.110 is

p~ 0.122

0.82 0.0147

The power of the test is

power = P(z > 0.82) = 1 - P(z <= 0.82) = 0.2061