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 65−74 years: n = 114, x = 11.3, and s = 6.65. Does this data indicate that average daily zinc intake in the population of all males age 65−74 falls below the recommended allowance? (Use α = 0.05.)
State the appropriate null and alternative hypotheses.

H₀: μ = 15
H_a: μ ≤ 15

H₀: μ = 15
H_a: μ < 15    

H₀: μ = 15
H_a: μ ≠ 15

H₀: μ = 15
H_a: μ > 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.)

z	=
P-value	=

State the conclusion in the problem context.

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.    

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.

Answer 1

H0: = 15

Ha: < 15

Test statistics

z = - / S / sqrt(n)

= 11.3 - 15 / 6.65 / sqrt(114)

= -5.94

p-value = p( Z < z)

= P( Z < -5.94 )

= 0

Since p-value < 0.05 level, we have sufficient evidence to reject H0.

Conclusion - Reject the null hypothesis. There is sufficient evidence that average daily zinc intake

falls below 15 mg / day.