A peanut farmer claims that the variance in the toxin level in his crops is 4.2 ppm (parts per million).A sample of 61 batches of peanuts reveals levels of 24.17 ppm on average, with a variance of 4.25 ppm. Conduct an appropriate hypothesis test to determine at the 0.05 level of significance if the farmer is correct. Assume a normal distribution.

Q4 (A) A health care magazine claims that a low-carbohydrate diet is more effective than a lowfat diet for weight loss. A sample of 77 people went on a low-carbohydrate diet for six months. At the end of that time the sample mean weight loss was 4.7 kg with a sample standard deviation of 7.2 kg. A second sample of 79 people went on a low-fat diet. Their sample mean weight loss was 2.6 kg with a standard deviation of 5.9 kg. Can you conclude at =0.05 that the mean weight loss is greater for those on the low-fat diet.

(B) In an experiment to test the effectiveness of a new sleeping aid, a sample of 12 patients took the new drug and a sample of 14 patients took a commonly used drug. Of the patients taking the new drug, the average time to fall asleep was 27.3 minutes with a standard deviation of 5.2 minutes. For the patients taking the commonly used drug the average time was 32.7 minutes with a standard deviation of 4.1 minutes. Can you conclude (as the manufacturer of the new drug claims) at =0.05 that the mean time to sleep is less for the new drug. Assume approximately normal distributions with equal variances.