Question: Answer all sections of this question:

a) A businessman claims that his company tapped for Initial Public Offering would make a profit of $20 million this year. If average profits for ten years are computed to be $19.4 million with an SD of $ 900,000.

i. Stating clearly the steps you have taken, write a possible null hypothesis that can be tested for this case scenario.

ii. Assuming the distribution of the profits to be normal, and with only this information, what test would you perform (explain your choice)

iii. Test the hypothesis against a significance level of 0.05 if continuous iv. Test the hypothesis against a significance level of 0.05 if discrete.

b) In a survey (Q 5 (b) above) of buying habits, 200 women shoppers are chosen at random in market X located in a certain section of the city. Their average weekly food expenditure is $100 with SD = $10. Another 200 women shoppers chosen similarly in market Y in another section of the city, the average weekly food expenditure is $75 with SD = $20. Calculate the confidence interval of the spending of each group then test at the level of significance of 0.05, whether the average weekly expenditure on food for the two groups of shoppers from which the samples were obtained are equal.