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 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.

Answer 1

Answer:

Step-by-step explanation:

a) H0: $\bar x = 24.57$

Ha: $\bar x \neq 24.57$

(Two tailed test at 5% significance level)

b) n=30

Mean difference = $23.89-24.57 = - 0.68$

Std error of mean = $\frac{s}{\sqrt{n} } \\=\frac{2.40}{\sqrt{30} } \\=0.4382$

b) Test statistic t = mean diff/std error = -1.552

df = 30-1 =29

p value=0.0657

c) Since p > 0.05 our signi. level, we accept null hypothesis.

There is no significant difference between the means.

d) Using critical value we find that test statistic is > critical value left

So accept H0