#3 It must be in the format of the second picture. The document appears to be related to a statistics problem involving the calculation of probabilities based on sample data.**Heading:** Statistical Problem Solving**Random Variable:** $\bar{X}$**Given:**\[ P(\bar{X} \leq 6820) = 0.0030 \]**Question:**Calculate the probability and evaluate using the given sample and population data.**Sample Data:**- Sample size ($n$): 50- Sample mean ($\bar{x}$): 6820**Sampling Distribution:**- **Type:** Normal- **Justification:** Central Limit Theorem (CLT), because $n > 30$- **Test Statistic:** $Z$- Calculation of test statistic: \[ \mu_{\bar{x}} = \mu = 7500 \\ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{1750}{\sqrt{50}} = 247.4874 \] \[ Z = \frac{\bar{x} - \mu_{\bar{x}}}{\sigma_{\bar{x}}} = \frac{6820 - 7500}{247.4874} = -2.75 \]**Population Data:**- Population mean ($\mu$): 7500- Population standard deviation ($\sigma$): 1750**C. Drawing Conclusions:**- Probability: \[ P(\bar{X} \leq 6820) = P(Z \leq -2.75) \approx 0.0030 \]**Graphical Explanation:**- A bell curve representing the normal distribution is drawn.- The area to the left of $Z = -2.75$ is shaded, indicating the probability of $\bar{X} \leq 6820$.**Calculator Display:**- The calculator is used for computations, showing values and operations corresponding to the calculation of the Z-score.This example illustrates how to use the Central Limit Theorem to approximate probabilities in a sampling distribution. The problem demonstrates the calculation of the Z-score and finding the related probability using the standard normal distribution. ### Statistical Problem Solving in Educational Contexts**Problem 3: Analyzing Blood Chemical Concentration**- **Context:** A random variable represents the concentration of chemical Z in human blood. A concentration level of 12% or more is considered unhealthy.- **Task:** Given a sample of 12 blood analyses with an average concentration of 13% and standard deviation of 1.3%, determine: - a. If there is statistical evidence to suggest a population mean higher than 12% for this patient. Use a significance level (α) of 5%. - b. Calculate a 99% confidence interval for the population mean. Perform this calculation on a separate paper.**Problem 4: Graduation Rate of Women Athletes**- **Context:** The long-term graduation rate for women athletes at a university is 67%. Recent data shows that 21 out of a sample of 38 women athletes graduated.- **Task:** Determine if the population proportion of women athletes graduating has changed. Use a 1% significance level.**Problem 5: Fishing Efficiency from Shore Versus Boat**- **Context:** A study has been conducted to determine whether it's more effective to fish from a boat or the shore. The variable of interest is the number of hours taken to catch a fish, recorded over several months.- **Data Table:** - **B (shore):** - October: 1.6 - November: 2.0 - December: 2.2 - January: 3.0 - February: 3.6 - March: 3.9 - April: 3.3 - **A (boat):** - October: 1.4 - November: 1.4 - December: 1.6 - January: 2.2 - February: 3.0 - March: 3.0 - April: 3.8- **Task:** Evaluate if there's a significant difference in mean fishing hours between the shore and the boat using a 1% significance level (paired difference test).**Problem 6: Hay Fever Rate Comparison**- **Context:** A comparison of hay fever rates per 1000 population in two different sample groups.- **Sample Details:** - **Sample 1:** Contains people under

Thus, we can say that the data suggest that the population mean μ is higher than 12% for this patient.

Answered: 3 It must be in the format of the…

Math

Statistics

3 It must be in the format of the second picture.

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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Question

#3 It must be in the format of the second picture.

The document appears to be related to a statistics problem involving the calculation of probabilities based on sample data.

**Heading:** Statistical Problem Solving

**Random Variable:** $\bar{X}$

**Given:**
\[ P(\bar{X} \leq 6820) = 0.0030 \]

**Question:**
Calculate the probability and evaluate using the given sample and population data.

**Sample Data:**
- Sample size ($n$): 50
- Sample mean ($\bar{x}$): 6820

**Sampling Distribution:**
- **Type:** Normal
- **Justification:** Central Limit Theorem (CLT), because $n > 30$
- **Test Statistic:** $Z$
- Calculation of test statistic:
\[
\mu_{\bar{x}} = \mu = 7500 \\
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{1750}{\sqrt{50}} = 247.4874
\]
\[
Z = \frac{\bar{x} - \mu_{\bar{x}}}{\sigma_{\bar{x}}} = \frac{6820 - 7500}{247.4874} = -2.75
\]

**Population Data:**
- Population mean ($\mu$): 7500
- Population standard deviation ($\sigma$): 1750

**C. Drawing Conclusions:**
- Probability:
\[
P(\bar{X} \leq 6820) = P(Z \leq -2.75) \approx 0.0030
\]

**Graphical Explanation:**
- A bell curve representing the normal distribution is drawn.
- The area to the left of $Z = -2.75$ is shaded, indicating the probability of $\bar{X} \leq 6820$.

**Calculator Display:**
- The calculator is used for computations, showing values and operations corresponding to the calculation of the Z-score.

This example illustrates how to use the Central Limit Theorem to approximate probabilities in a sampling distribution. The problem demonstrates the calculation of the Z-score and finding the related probability using the standard normal distribution.

### Statistical Problem Solving in Educational Contexts

**Problem 3: Analyzing Blood Chemical Concentration**
- **Context:** A random variable represents the concentration of chemical Z in human blood. A concentration level of 12% or more is considered unhealthy.
- **Task:** Given a sample of 12 blood analyses with an average concentration of 13% and standard deviation of 1.3%, determine:
- a. If there is statistical evidence to suggest a population mean higher than 12% for this patient. Use a significance level (α) of 5%.
- b. Calculate a 99% confidence interval for the population mean. Perform this calculation on a separate paper.

**Problem 4: Graduation Rate of Women Athletes**
- **Context:** The long-term graduation rate for women athletes at a university is 67%. Recent data shows that 21 out of a sample of 38 women athletes graduated.
- **Task:** Determine if the population proportion of women athletes graduating has changed. Use a 1% significance level.

**Problem 5: Fishing Efficiency from Shore Versus Boat**
- **Context:** A study has been conducted to determine whether it's more effective to fish from a boat or the shore. The variable of interest is the number of hours taken to catch a fish, recorded over several months.
- **Data Table:**
- **B (shore):**
- October: 1.6
- November: 2.0
- December: 2.2
- January: 3.0
- February: 3.6
- March: 3.9
- April: 3.3
- **A (boat):**
- October: 1.4
- November: 1.4
- December: 1.6
- January: 2.2
- February: 3.0
- March: 3.0
- April: 3.8
- **Task:** Evaluate if there's a significant difference in mean fishing hours between the shore and the boat using a 1% significance level (paired difference test).

**Problem 6: Hay Fever Rate Comparison**
- **Context:** A comparison of hay fever rates per 1000 population in two different sample groups.
- **Sample Details:**
- **Sample 1:** Contains people under

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