Question

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. a. State the null hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. 2. 3. Choose correct answer from above choice State the alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. 2. 3. Choose correct answer from above choice b. Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value. Round your answer to four decimal places. c. With = .05 as the level of significance, what is your conclusion? p-value .05, H 0. We that the population mean hourly wage for manufacturing workers the population mean of $24.57 for the goods-producing industries. d. Repeat the preceding hypothesis test using the critical value approach. Round your answer to two decimal places. Enter negative values as negative numbers. z = ; H 0

Answer 1

(a) The Null Hypothesis: H0: = 24.57

The Alternative hypothesis: Ha: 24.57

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(b) = $23.89, = $2.40, n = 30,

The Test statistic:

The p value (2 tails) at z = -1.55 is; p- value = 0.1211

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(c) Since p value is > , We Fail To Reject H0.

Therefore We dont have sufficient evidence to conclude that the population mean hourly wage for manufacturing workers is different from the population mean of $24.57 for the goods - producing industries.

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(d) Z observed as calculated in (c) = -1.55.

The Z critical (2 tail) at = 0.05 is -1.96 and +1.96

Since Zobserved lies in between -1.96 and +1.96, we fail to reject H0.

Therefore We dont have sufficient evidence to conclude that the population mean hourly wage for manufacturing workers is different from the population mean of $24.57 for the goods - producing industries.

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