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 4.1 mg. Preliminary data analyses indicate that applying the z-test is reasonable. (Note: x= 14.67 mg.) Click here to view the iron intake data. Click here to view Page 1 of the table of areas under the standard normal curve. Click here to view Page 2 of the table of areas under the standard normal curve. State the hypotheses for the one-mean z-test. HoH mg Ha mg (Type integers or decimals as needed. Do not round.) Compute the value of the test statistic. za (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) O A. The critical value is za = OB. The critical value is - Zx = O C. The critical values are + 2a/2 = + - the null hypothesis. At the 10% significance level, the data sufficient evidence to conclude that adult females are the RDA of iron, on average. Click to select your answer(s).

Answer 1

Given that, x = 14.67,0 =4.1, n = 45 Null and the alternative hypothesis: H: 18 H: <18 Significance level, a =0.10 Test statistic: X- 14.67-18 4.1 145 =-5.45 Critical value: By using z tables, the critical value of z at 10% level of significance for left tailed test is, -20.05 =-1.28 Decision rule: Reject H, if z<-za or do not reject H || Since the test statistic value is less than critical value, we reject the null hypothesis at the specified level of significance. Conclusion: Reject the null hypothesis. At the 10% significance level, the data provide sufficient evidence to conclude that adult females are less than the RDA of 18 mg of iron on average