A consumer watchdog group suspects that a yogurt that is advertised to be 98% fat free has in fact a higher mean fat content. The group will take action against the company if it can substantiate its suspicion with factual data. To do so, the consumer group takes a sample of 25 yogurt cups (each containing 170 grams) and measures the fat contents. The sample mean fat content for 25 sample cups is 3.6 grams and the sample standard deviation is 0.8 grams. Suppose that the mean fat content for 25 sample cups was 3.6 grams. Also that σ=0.5 grams. Requried:
a. Do α= 0.01 level test of the hypotheses. Use p- value and the critical value approach.
b. Is there enough statistical evidence to support the consumer group’s suspicion?