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4. A marketing research used a sample of 12 individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. (a) Construct a 95% confidence interval for the mean, ld, of the population paired differences, where a paired difference is equal to the purchase potential rating before seeing the TV commercial minus the purchase potential rating after seeing the TV commercial. Interpret your results. (b) Using the 1% significance level, can you conclude that this TV commercial significantly increases the purchase potential ratings? (19 marks)