Someone can help me to figure out this Math question? The recommended daily diet

Question

Someone can help me to figure out this Math question?

The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. The article "Nutrient Intakes and Dietary Patterns of Older Americans: A National Study" (J. of Gerontology, 1992: M145-150) reports the following summary data on intake for a sample of males age 65-74 years: n=l 15, x = 11.3, and s=6.43. Does this data indicate that average daily zinc intake in the population of all males' ages 65-74 falls below the recommended allowance? Are the t-based procedures (CI and hypothesis test) appropriate for this data? Justify your answer. State the null and alternative hypotheses. Calculate the test statistic. Define the rejection region at alpha=0.05. Make a decision about the test. Find the p-value corresponding to the test and make a conclusion.

Explanation / Answer

Yes here we use t-test for one sample.

Because population standard deviation is unknown.

The test of hypothesis is,

H0 : mu = 15 Vs H1 : mu < 15

where mu is the population mean.

Assume alpha = 0.05

mu0 = 15

n = 115

Xbar = 11.3

sd = 6.43

We can done this test in MINITAB.

steps :

STAT --> TESTS --> 2:T-Test --> ENTER --> Inpt : Highlight on Stats --> ENTER --> Input mu0, Xbar, Sx and n --> Select "<mu0" --> ENTER --> Calculate --> ENTER

The t-test statistic is,

t = -6.17

P-value = 5.33756E-9 = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The data indicate that average daily zinc intake in the population of all males ages 65-74 falls below the recommanded allowance.

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