Question

The recommended daily allowance of iron for females aged 19–50 is 18 mg/day. A careful measurement of the daily iron intake of 15 women yielded a mean daily intake of 16.2 mg with sample standard deviation 4.7 mg.

a. Assuming that daily iron intake in women is normally distributed, perform the test that the actual mean daily intake for all women is different from 18 mg/day, at the 10% level of significance.

b. The sample mean is less than 18, suggesting that the actual population mean is less than 18 mg/day. Perform this test, also at the 10% level of significance. (The computation of the test statistic done in part (a) still applies here.)

Answer 1

a)

H0: = 18

Ha: 18

Test statistics

z = ( - ) / ( S / sqrt(n) )

= ( 16.2 - 18) / (4.7 / sqrt(15) )

= -1.48

df = n - 1 = 15 - 1 = 14

From T table,

t critical values at 0.10 significance level with 14 df = -1.761 , 1.761

Since test statistics falls in non-rejection region, Do not reject H0

We conclude that we fail to support the claim that mean daily intake for all women is different

from 18 mg/day.

b)

Calculated test statistics = -1.48

One tailed t critical value at 0.10 significance level with 14 df = -1.345

Since test statistics < -1.345, reject H0

We conclude that we have sufficient evidence to support the claim that mean daily intake for

all women is less than 18 mg/day.