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 1% 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= 14.65 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) Ho: H Ha: mg mg (Type integers or decimals as needed. Do not round.) 14.5 18.6 14.4 14.4 10.7 18.3 18.5 18.6 14.6 O Compute the value of the test statistic. 15.7 12.9 16.5 20.4 19.1 11.5 13.2 15.9 11.0 14.9 9.6 19.5 18.8 14.2 16.5 11.6 15.8 12.6 14.0 11.7 12.1 19.0 13.O 11.9 10.7 18.0 12.4 (Round to two decimal places as needed.) 17.3 6.4 16.8 12.1 16.4 14.8 13.1 15.7 11.6 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 values are tZ/2 =+ Print Done O B. The critical value is - Z,= O C. The critical value is z, =
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 1% 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= 14.65 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) Ho: H Ha: mg mg (Type integers or decimals as needed. Do not round.) 14.5 18.6 14.4 14.4 10.7 18.3 18.5 18.6 14.6 O Compute the value of the test statistic. 15.7 12.9 16.5 20.4 19.1 11.5 13.2 15.9 11.0 14.9 9.6 19.5 18.8 14.2 16.5 11.6 15.8 12.6 14.0 11.7 12.1 19.0 13.O 11.9 10.7 18.0 12.4 (Round to two decimal places as needed.) 17.3 6.4 16.8 12.1 16.4 14.8 13.1 15.7 11.6 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 values are tZ/2 =+ Print Done O B. The critical value is - Z,= O C. The critical value is z, =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![This image contains a fill-in-the-blank statement related to hypothesis testing in statistics. The statement reads as follows:
"[Dropdown 1] the null hypothesis. At the 1% significance level, the data [Dropdown 2] sufficient evidence to conclude that adult females are [Dropdown 3] the RDA of iron, on average."
Explanation:
- **Dropdown 1**: This likely includes options related to decisions about the null hypothesis, such as "accept" or "reject."
- **Dropdown 2**: This may provide choices about the sufficiency of the evidence, such as "does" or "does not" indicate.
- **Dropdown 3**: This could have options like "meeting," "exceeding," or "not meeting" to describe the status of iron intake relative to the Recommended Dietary Allowance (RDA).
The educational context likely involves understanding how to interpret statistical results and draw conclusions based on hypothesis testing principles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b425c8-1e3a-4bc4-9526-e999f44a089d%2Ff3c48da2-d628-4889-af63-73d9f4b855e2%2Fn2eum0gp_processed.png&w=3840&q=75)
Transcribed Image Text:This image contains a fill-in-the-blank statement related to hypothesis testing in statistics. The statement reads as follows:
"[Dropdown 1] the null hypothesis. At the 1% significance level, the data [Dropdown 2] sufficient evidence to conclude that adult females are [Dropdown 3] the RDA of iron, on average."
Explanation:
- **Dropdown 1**: This likely includes options related to decisions about the null hypothesis, such as "accept" or "reject."
- **Dropdown 2**: This may provide choices about the sufficiency of the evidence, such as "does" or "does not" indicate.
- **Dropdown 3**: This could have options like "meeting," "exceeding," or "not meeting" to describe the status of iron intake relative to the Recommended Dietary Allowance (RDA).
The educational context likely involves understanding how to interpret statistical results and draw conclusions based on hypothesis testing principles.
![### Hypothesis Testing for Iron Intake in Adult Females
The recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. We are given iron intake data for 45 random adult females and are tasked with determining if, on average, females get less than the RDA of 18 mg of iron.
**Dataset Provided:**
- A sample mean (\( \bar{x} \)) of 14.65 mg
- Population standard deviation (\( \sigma \)) of 4.2 mg
**Hypothesis Statement:**
- Null Hypothesis (\( H_0 \)): \( \mu = 18 \) mg
- Alternative Hypothesis (\( H_a \)): \( \mu < 18 \) mg
**Compute the Z-test Statistic:**
To determine the Z-test statistic, use the formula:
\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \]
where:
- \( \bar{x} = 14.65 \)
- \( \mu = 18 \)
- \( \sigma = 4.2 \)
- \( n = 45 \)
**Critical Value Selection:**
At the 1% significance level, select the appropriate critical value for a one-tailed test:
- Option A: The critical values are \( z_{\alpha/2} = \pm \_\_ \).
- Option B: The critical value is \( -z_\alpha = \_\_ \).
- Option C: The critical value is \( z_\alpha = \_\_ \).
**Iron Intake Data Table:**
The values of iron intake (in mg per day) for the sample of 45 adult females are:
\[
\begin{array}{cccccc}
14.5 & 18.6 & 14.4 & 14.4 & 10.7 & 18.5 \\
18.6 & 14.6 & 15.7 & 12.9 & 16.5 & 20.4 \\
19.1 & 18.3 & 13.2 & 15.9 \\
11.0 & 14.9 & 9.6 & 9.5 & 11.8 & 15.4 \\
18.3 & 12.6 & 14.0 & 11.7 & 12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b425c8-1e3a-4bc4-9526-e999f44a089d%2Ff3c48da2-d628-4889-af63-73d9f4b855e2%2F6c8y0d8_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Iron Intake in Adult Females
The recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. We are given iron intake data for 45 random adult females and are tasked with determining if, on average, females get less than the RDA of 18 mg of iron.
**Dataset Provided:**
- A sample mean (\( \bar{x} \)) of 14.65 mg
- Population standard deviation (\( \sigma \)) of 4.2 mg
**Hypothesis Statement:**
- Null Hypothesis (\( H_0 \)): \( \mu = 18 \) mg
- Alternative Hypothesis (\( H_a \)): \( \mu < 18 \) mg
**Compute the Z-test Statistic:**
To determine the Z-test statistic, use the formula:
\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \]
where:
- \( \bar{x} = 14.65 \)
- \( \mu = 18 \)
- \( \sigma = 4.2 \)
- \( n = 45 \)
**Critical Value Selection:**
At the 1% significance level, select the appropriate critical value for a one-tailed test:
- Option A: The critical values are \( z_{\alpha/2} = \pm \_\_ \).
- Option B: The critical value is \( -z_\alpha = \_\_ \).
- Option C: The critical value is \( z_\alpha = \_\_ \).
**Iron Intake Data Table:**
The values of iron intake (in mg per day) for the sample of 45 adult females are:
\[
\begin{array}{cccccc}
14.5 & 18.6 & 14.4 & 14.4 & 10.7 & 18.5 \\
18.6 & 14.6 & 15.7 & 12.9 & 16.5 & 20.4 \\
19.1 & 18.3 & 13.2 & 15.9 \\
11.0 & 14.9 & 9.6 & 9.5 & 11.8 & 15.4 \\
18.3 & 12.6 & 14.0 & 11.7 & 12
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