The claim that "42% of those persons who retired before the age of 65 would return to work if a suitable job was available," is to be investigated at the 0.05 level of significance. If 74 out of the 200 workers sampled said they would return to work, what is our decision? Question 5.2 (One sample mean test - 2) A quality manager of a soy sauce company is interested in testing whether the average soy sauce per bottle differs from the labeled amount of 200 ml. The manager samples 40 bottles, measures the volume of their contents and finds the sample mean is 197 ml. Assume the soy sauce per bottle follow normal distribution with a population standard deviation of 30 ml. At the 0.01 level of significance, is there evidence that the average soy sauce per bottle is less than 200 ml? Question 5.3 (One sample t test) The average cost of tuition fee at post-secondary colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 40 post-secondary colleges showed that the average cost per term is $8,945 with a standard deviation of $1,200. Test at 1% level of significance, is there evidence that the average cost of tuition is more than $ 8,500? Question 5.4 (Two sample proportion test-z) A sample of university students was asked as a part of a comprehensive survey whether they favored the newly proposed environmental policy. The results were: Number sampled Number in favor Male 1000 280 Female 800 198 At the 0.05 level of significance, can we conclude that there is a larger proportion of male students in favor of the newly proposed environmental policy? Question 5.5 (Two sample mean test - z) A financial planner wants to compare the yield of Income fund and Growth mutual fund. Fifty thousand dollars is invested in each of a sample of 35 Income funds and 40 Growth funds. The mean increase for a two-year period for the Income funds is $900. For the growth funds the mean increase is $875. Income finds have a population standard deviation of $30; Growth funds have a population standard deviation of $45. At the 0.02 significance level, is there a difference in the mean yields of the two funds?