Question

3. The wages (hourly) in a particular industry has are mandated to be normally distributed with mean $13.20 and standard deviation $2.50. One company in this industry employs 40 workers, and has an average hourly wage of $12.20. (a) Is there sufficient evidence to suggest that this company is paying substandard wages at the .01 level? (b) What is the probability that if we were to randomly select 40 workers from this industry, who were not being underpaid, that we would observe an average hourly wage of $12.20 or less? Leave your answer in terms of the distribution function of the standard normal distribution.

Answer 1

(a) The null and alternative hypotheses are; H: 4=13.20 Hu<13.20 This is a lower tailed test. The value of test statistic is, 2X- 12.20-13.20 2.5/ V40 =-2.53 The level of significance is 0.01. the z-critical value for lower tailed hypothesis is obtained as -2.33 using the standard normal table at 0.01 significance level. Since, the test statistic is smaller than the critical value, the null hypothesis is rejected. It can be concluded that there is sufficient evidence that the company can be accused of paying their workers substandard wages. (b) The required probability is, P(x512.20) = pſ 3-4 - 12.20-13 20 lolan 25 √40 , = P(23-2.53) (using the standard normal table) = 0.0057