Based on nutrition research, it has been reported that only 3% of children in the US ages 6 - 10 eat the recommended number of servings for all five major food groups each day. An official in a certain state claims that the value for their children ages 6 - 10 is above 3%. A random sample of 600 children in this age group in the state was obtained, and 27 were found to eat the recommended number of servings each day. Test the state official's claim more than 3% of children ages 6 - 10 in the state eat the recommended number of servings for all five major food groups each day at =0.04 by answering parts (a) - (e) below.

(a) Write the null and alternative hypotheses. Is the test left-tailed, right-tailed, or two-tailed.

(b) Assuming the random samples are independent (in other words, assuming n0.05N), verify that the sampling distribution is (approximately) normal.

(c) Find/calculate the test statistic, z₀.

(d) Find/calculate the P-value.

(e) State the conclusion, including reasoning through comparison of the P-value to .