A marketing research analyst collects data for a random sample of 100 customers out of the 4,000 who purchased a particular "coupon special." The 100 people spent a sample average of X = $24.57 in the store with a standard deviation of σ = $6.60. Before seeing these sample results, the marketing manager had claimed that the average purchase by those responding to the coupon offer would be at least (not less than) $25.00. Can this claim be rejected, using the 5 percent level of significance?
A survey conducted by a research institute lists median salaries for associate professors of statistics at public sector institutions and at private sector institutions in Pakistan. Assume that a sample of 100 associate professors from public sector institutions has an average salary of PKR 72,000 per month with a standard deviation of PKR 6,000. Assume also that a sample of 150 associate professors from private sector institutions has an average salary of PKR 78,000 with a standard deviation of PKR 5,000. Test the hypothesis that the mean salary for associate professors in private institutions is PKR 1,500 higher than for those in other institutions. Use a 0.01 level of significance.