Exercise 1 The Florida Department of Labor and Employment Security reported the state mean annual wage...

Exercise 1 The Florida Department of Labor and Employment Security reported the state mean annual wage was $26,133 (The Naples Daily News, February 13, 1999). A hypothesis test of wages by county can be conducted to see whether the mean annual wage for a particular county differs from the state mean. (a) A sample of 550 individuals in Collier County showed a sample mean annual wage of $25,457. Assume a population standard deviation σ = $7600. Is there enough evidence in this sample to say, at the 5% significance level, that in Collier County the salaries are, on average, lower than in the rest of the state? Specify the test you have to conduct. Find the statistic of the test and compare with the corresponding critical value. Explain your conclusion. (b) Find and interpret the p-value of the test. (c) Find the minimum average wage that would be necessary to reject the null at the 1% significance level in the following test: H0 : µ = $26, 133 H1 : µ > $26, 133 if we assume a sample of 400 individuals.

Solutions

Expert Solution

a) H0: The Collier County the salaries are, on average, not lower than in the rest of the state

H1: The Collier County the salaries are, on average, lower than in the rest of the state

i.e.

b) If sample size n = 400, he minimum average wage that would be necessary to reject the null at the 1% significance level in the following test: H0 : µ = $26, 133 H1 : µ > $26, 133 is

orchestra answered 1 year ago

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