Question

The recommended daily dietary allowance for zinc among men older than 50 (years) is 15 mg/day. In a random sample of 115 men ages 65-74, the sample mean was 11.3 mg/day and sample standard deviation was 6.43 mg/day. Does this suggest that average daily zinc intake of all men ages 65-74 is below the recommended allowance? Do a 4-part hypothesis test ((Hypotheses, assumptions, calculation and conclusion)with α = .01.

Show your work. For p-value use R code.

Answer 1

Since we want to check if average daily zinc intake of all men ages 65-74 is below the recommended allowance

this is left-tailed test

TS= (Xbar - mu)/(sd/sqrt(n))

= -6.170774

df =n-1 = 114

p-value = 0

since p-value < alpha, we reject the null hypothesis

we conclude that the this suggest that average daily zinc intake of all men ages 65-74 is below the recommended allowance

code in R

Xbar = 11.3
mu = 15
sd = 6.43
n = 115
TS <- (Xbar - mu)/(sd/sqrt(n))
TS
p_value = pt(TS,df =n-1)
p_value

Output