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 65-74 years: n = 115, x = 11.5, and s = 6.55. Does this data indicate that average daily zinc intake in the population of all males age 65-74 falls below the recommended allowance? (Use alpha = 0.05.) State the appropriate null and alternative hypotheses. Calculate the test statistic and determine the P-value. 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

Set Up Hypothesis
Null, H0: U=15
Alternate,average intake is below the actual population H1: U<15
Test Statistic
Population Mean(U)=15
Sample X(Mean)=11.5
Standard Deviation(S.D)=6.55
Number (n)=115
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=11.5-15/(6.55/Sqrt(115)
Zo =-5.7303
| Zo | =5.7303
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =5.7303 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -5.7303 ) = 0
Hence Value of P0.05 > 0, Here we Reject Ho

[answer]
Zo =-5.73
p= 0
Reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day.

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