Question: please help me with question; Could you please check if my work is correct; I got for 1, P=0.0139 (not enough evidence), for 2, Type

please help me with question;

Could you please check if my work is correct;

I got for 1, P=0.0139 (not enough evidence), for 2, Type II error =0.997, for 3 sample size=354

The recommended daily dietary allowance for zinc among males older than age 50 is 15 mg/day. A National Study collected a sample of 50 males age between 65 and 74 and the sample mean is = 13. Suppose data are normal and the population standard deviation = 6.43. Does this study indicate that average daily zinc intake in the population of all males ages 65-74 falls below the recommended allowance? (Use = 0.05) i) (8 pts) Test the hypothesis that average daily zinc intake in the population of all males ages 65-74 falls below the recommended allowance. ii) (3 pts) What is the type II error rate (-value) for the test if the true mean daily zinc intake is 16? iii) (3 pts) What sample size would be required to ensure that does not exceed 0.1 if the true mean value is 16?

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