Answer Happy

a) A random sample of 85 men revealed that they spent a mean of 6.5 years in school. The standard deviation from this sample was 1.7 years. (i) Construct a 95\% Confidence Interval for the population mean and interpret your answer. [4 marks] (ii) Suppose the question in part (i) had asked to construct a 99\% confidence interval rather than a 95\% confidence interval. Without doing any further calculations, how would you expect the confidence interval to change? [3 marks] (iii) You want to estimate the mean number of years in school to within 0.5 year with 98% confidence. How many men would you need to include in your study? [3 marks] (b) A Public Health Inspector took a random sample of 120 perishable food items from the shelves of a supermarket. Of these items, 6 had exceeded their "best before" date. Use a statistical hypothesis testing procedure to determine if the proportion of perishable food items exceeding their "best before" date is higher than 3.5%. Use a 5% level of significance. Clearly state the null and alternative hypothesis, the test statistic, the critical value from the table, the p-value, the decision, and conclusion. [15 marks]