Question

The recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. The given iron intakes (mg) were obtained for 45 random adult females. At the 10% significance level, do the data suggest that adult females are, on average, getting less than the RDA of 18 mg of iron? Assume that the population standard deviation is 4.2 mg. Preliminary data analyses indicate that applying the z-test is reasonable. (Note: x bar equals=14.65 mg.)

1. State the hypotheses for the​ one-mean z-test.
2. Compute the value of the test statistic. z=______
3. Determine the critical​ value(s).
4._________ the null hypothesis. At the 10​% significance​ level, the data____________sufficient evidence to conclude that adult females are ___________ the RDA of​ iron, on average.

Answer 1

Explanation:

Given that the recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. The given iron intakes (mg) were obtained for 45 random adult females.

`n =45\\\bar x = 14.65\\\sigma = 4.2\\std error = (4.2)/(√(45) ) \\=0.6261`

1)
`H_0: \bar x =18\\H_a: \bar x <18`

(left tailed test at 10% sigl level)

Mean difference = -3.35

2) Test statistic Z = Mean difference/std error =-5.35

3) Critical values are -1.28

Since critical value is > test statistic accept H0

4) ___Fail to reject______ the null hypothesis. At the 10​% significance​ level, the data_____shows_______sufficient evidence to conclude that adult females are ____equal to 18 mg_______ the RDA of​ iron, on average.