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 5% 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=14.68 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. - X Iron intake (mg per day) H V mg H V mg (Type integers or decimals 152 17.7 14.2 14.4 10.5 18.5 18.3 17.8 15.3 O needed. Do not round.) 16.2 12.7 17.2 21.0 19.7 11.9 124 16.2 10.6 Compute the value of the test statistic. 14.8 9.3 19.6 18.0 15.1 16.8 11.8 16.7 12.9 14.4 11.6 12.8 19.1 12.7 12.3 10.4 17.1 12.0 17.6 62 16.1 12.2 16.3 14.3 12.9 16.8 11.1 (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 -z= Print Done O B. The critical values are +z/2 = : OC. The critical value is z=

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**Overview of Iron Intake Analysis**

The recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. A study was conducted to assess whether adult females' iron intake is less than the RDA. Iron intakes (mg per day) were collected from 45 random adult females.

**Data Summary:**
The sample mean iron intake is 14.68 mg, and the population standard deviation is assumed to be 4.2 mg. A z-test is being used to analyze the data at a 5% significance level.

**Iron Intake Data (mg per day):**

```
15.2, 17.7, 14.2, 14.4, 10.5, 18.3, 17.8, 15.3
16.2, 12.7, 12.7, 21.0, 19.7, 11.9, 12.4, 12.7
14.8, 9.3, 13.1, 17.7, 14.4, 16.2, 11.0, 14.4
14.4, 11.6, 12.4, 10.3, 16.7, 12.5, 11.3
17.6, 6.2, 16.1, 12.1, 13.4, 12.9, 16.8, 11.1
```

**Hypotheses for One-Mean z-Test:**
- Null Hypothesis (H₀): μ = 18 mg
- Alternative Hypothesis (Hₐ): μ < 18 mg

**Calculation of Test Statistic:**
The test statistic, z, should be rounded to two decimal places.

**Determination of Critical Value:**
Options for critical value determination include selecting from:
- A specified critical value 
- A range critical value zᵤ/₂ = ± [value]
- A direct critical value zₐ = [value]

**Conclusion Process:**
The null hypothesis is either rejected or not rejected based on the test results. At the 5% significance level, you can determine if there's sufficient evidence to conclude that adult females intake is less than the RDA of iron, on average.

---

This educational section guides learners through hypothesis testing for determining if
Transcribed Image Text:**Overview of Iron Intake Analysis** The recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. A study was conducted to assess whether adult females' iron intake is less than the RDA. Iron intakes (mg per day) were collected from 45 random adult females. **Data Summary:** The sample mean iron intake is 14.68 mg, and the population standard deviation is assumed to be 4.2 mg. A z-test is being used to analyze the data at a 5% significance level. **Iron Intake Data (mg per day):** ``` 15.2, 17.7, 14.2, 14.4, 10.5, 18.3, 17.8, 15.3 16.2, 12.7, 12.7, 21.0, 19.7, 11.9, 12.4, 12.7 14.8, 9.3, 13.1, 17.7, 14.4, 16.2, 11.0, 14.4 14.4, 11.6, 12.4, 10.3, 16.7, 12.5, 11.3 17.6, 6.2, 16.1, 12.1, 13.4, 12.9, 16.8, 11.1 ``` **Hypotheses for One-Mean z-Test:** - Null Hypothesis (H₀): μ = 18 mg - Alternative Hypothesis (Hₐ): μ < 18 mg **Calculation of Test Statistic:** The test statistic, z, should be rounded to two decimal places. **Determination of Critical Value:** Options for critical value determination include selecting from: - A specified critical value - A range critical value zᵤ/₂ = ± [value] - A direct critical value zₐ = [value] **Conclusion Process:** The null hypothesis is either rejected or not rejected based on the test results. At the 5% significance level, you can determine if there's sufficient evidence to conclude that adult females intake is less than the RDA of iron, on average. --- This educational section guides learners through hypothesis testing for determining if
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