Question

Using a .05 level of significance, what is your conclusion? 17. 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 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. b. Suppose a sample of 30 employees from the manufacturing industry showed a sam- ple mean of $23.89 per hour. Assume a population standard devia

Answer 1

We conclude that the the population mean hourly wage in the manufacturing industry does not differ from the population mean hourly wage in the goods-producing industries.

Explanation:

We are given that the mean hourly wage for employees in goods-producing industries is currently $24.57.

Let
`\mu` = population mean hourly wage in the manufacturing industry

(a) Null Hypothesis,
`H_0` :
`\mu` = $24.57 {means that the population mean hourly wage in the manufacturing industry does not differ from the population mean hourly wage in the goods-producing industries}

Alternate Hypothesis,
`H_1` :
`\mu\\eq` $24.57 {means that the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries}

The test statistics that will be used here is One-sample z-test statistics because we know about the population standard deviation;

T.S. =
`(\bar X-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where,
`\bar X` = sample mean hourly wage = $23.89 per hour

`\sigma` = population standard deviation = $2.40 per hour

n = sample of employees = 30

So, the test statistics =
`(\$23.89-\$24.57)/((\$2.40)/(√(30) ) )`

= -1.55

The value of z-test statistics is -1.55.

Now, at a 5% level of significance, the z table gives a critical value between -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the the population mean hourly wage in the manufacturing industry does not differ from the population mean hourly wage in the goods-producing industries.