Question

Asked Mar 1, 2019

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 and alternative hypothesis we should use to test whether the population mean hourly wage in the manufacturing industry to see if the mean hourly wage differs from the population mean hourly wage in the goods-producing industries.

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.

C. With = .05 as the level of significance, what is your conclusion?

D. Repeat the preceding hypothesis test using the critical value approach.

Step 1

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Given that mean hourly wages for employees is $24.57.

We are testing to see if the population mean hourly wage is different from $24.57. So, this is a two tail test.

Null Hypothesis : H_{0} : µ_{0} = 24.57

Alternate Hypothesis : H1 : µ_{1} ≠ 24.57

Step 2

Given a sample of 30 employees and populaiton standard deviaiton = 2.4 and sample mean =23.89

SInce population standard deviation is known we use Z test.

The test statistic Z can be calculated by below mentioned formula. Bysubstituting values µ_{0} = 24.57 Xbar = 23.89, σ = 2.4 aand n = 30. We get Z = -1.55

test statistic Z = -1.55

Step 3

With reference to Z table we can see the P( Z < -1.55) = 0.0606

Since this is two tail test p value is shown in figure below and we know left tail for ...

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