I need some help with this question in statistics

(20 pts) 7. The value used for the mean amount of fat in one portion of a prepackaged food item is 20 grams. With the introduction of a new production process the manufacturer must investigate whether this claim is true or not. A sample of 70 portions sample mean 20.2 grams with sample standard deviation .4 grams. Assume the population is normally distributed. (5 pts) a. State the null and alternative hypotheses for the test. (5 pts) b. State the correct formula for the test statistic. Compute the value of the test statistic. (5 pts) c. Make a decision based on the context at 5% signicance level. (5 pts) d. Compute a 95% condence interval for the mean fat content of portions. Bonus Question (5 pts) If X has a normal distribution with mean ,u and standard deviation 0'2, prove that Z = (X p) [a has a stande normal distribution with mean 0 and variance 1. Hint: (Show that E(Z)=0 and V(Z)=l, where pi and a" are constants here. Then any linear combination of normal random variables is also normally distributed.)