Question

Q3: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 sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value.c.With 훼=0.05as the level of significance, what is your conclusion?d.Repeat thepreceding hypothesis test using the critical value approach.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 24.57
Alternative Hypothesis: μ ≠ 24.57

b)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (23.89 - 24.57)/(2.4/sqrt(30))
z = -1.55

c)

P-value Approach
P-value = 0.1211

As P-value >= 0.05, fail to reject null hypothesis.

d)

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (23.89 - 24.57)/(2.4/sqrt(30))
z = -1.55

As the value of test statistic, z is within critical value range, fail to reject the null hypothesis