The recommended daily dietary allowance for zinc among males older than age 50 y

Question

The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. An article reports the following summary data on intake for a sample of males age 6574 years: n = 115, x = 12.1, and s = 6.50. Does this data indicate that average daily zinc intake in the population of all males age 6574 falls below the recommended allowance? (Use = 0.05.)
State the appropriate null and alternative hypotheses.

H0: = 15
Ha: 15H0: = 15
Ha: < 15    H0: = 15
Ha: > 15H0: = 15
Ha: 15

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

State the conclusion in the problem context.

Reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day.

Do not reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day.    

Reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day.

Do not reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day.

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 15
HA : < 15
Standard deviation = 6.5

Hypothesis test results:

Hence,

H0: = 15
Ha: < 15

z = -4.78

p - Value = 0.0000

Reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day. Option A

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