The average or mean hourly wage in a selected province is $10.05. A sample of 25 workers has been taken. The mean hourly wage in the sample is $10.83 with a sample standard deviation of $3.25 per hour. Do a two-sided test of hypothesis to test if the true mean population wage in the province is indeed $10.05. Use a 20% level of significance.

a) Set up the null and alternative hypothesis using a two-sided test.

b) State the critical value which separate the acceptance and rejection regions.

c) Evaluate the proper test statistic.

d) Would you accept or reject the null hypothesis. Explain