We want to conduct a hypothesis test of the claim that for middle-aged adults the population mean of their cholesterol levels is more than 195.8 mgdL. We choose a random sample of such levels. The sample has a mean of 190.8 mgdL and a standard deviation of 18 mgdL. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. ### Understanding Which Test Statistic to Use#### (a) Scenario: Large Sample from a Non-Normally Distributed Population- **Description**: The sample has a size of 100, and it is drawn from a non-normally distributed population with a known standard deviation of 19.2.- **Options to Consider**: - Use the z-statistic: \( \circ \ z = \_\_\_ \) - Use the t-statistic: \( \circ \ t = \_\_\_ \) - It is unclear which test statistic to use: \( \circ \ \text{It is unclear which test statistic to use.} \)#### (b) Scenario: Small Sample from a Normally Distributed Population- **Description**: The sample has a size of 10, and it is drawn from a normally distributed population with an unknown standard deviation.- **Options to Consider**: - Use the z-statistic: \( \circ \ z = \_\_\_ \) - Use the t-statistic: \( \circ \ t = \_\_\_ \) - It is unclear which test statistic to use: \( \circ \ \text{It is unclear which test statistic to use.} \)### ExplanationFor each scenario, choose the appropriate test statistic based on sample size, population distribution, and whether the population standard deviation is known:- **For large samples (typically n > 30)**: - If the population standard deviation is known, the z-statistic is generally used. - **For small samples (n ≤ 30)**: - If the population is normally distributed and the standard deviation is unknown, the t-statistic is typically more appropriate.In these scenarios, ensure that you apply these principles to determine the correct test statistic.

Given: Hypothesized Mean (µ0) = 195.8 Sample mean is X = 190.8 Population…

Answered: We want to conduct a hypothesis test of…

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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We want to conduct a hypothesis test of the claim that for middle-aged adults the population mean of their cholesterol levels is more than 195.8 mgdL. We choose a random sample of such levels. The sample has a mean of 190.8 mgdL and a standard deviation of 18 mgdL. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places.

### Understanding Which Test Statistic to Use

#### (a) Scenario: Large Sample from a Non-Normally Distributed Population

- **Description**: The sample has a size of 100, and it is drawn from a non-normally distributed population with a known standard deviation of 19.2.
- **Options to Consider**:
- Use the z-statistic: \( \circ \ z = \_\_\_ \)
- Use the t-statistic: \( \circ \ t = \_\_\_ \)
- It is unclear which test statistic to use: \( \circ \ \text{It is unclear which test statistic to use.} \)

#### (b) Scenario: Small Sample from a Normally Distributed Population

- **Description**: The sample has a size of 10, and it is drawn from a normally distributed population with an unknown standard deviation.
- **Options to Consider**:
- Use the z-statistic: \( \circ \ z = \_\_\_ \)
- Use the t-statistic: \( \circ \ t = \_\_\_ \)
- It is unclear which test statistic to use: \( \circ \ \text{It is unclear which test statistic to use.} \)

### Explanation

For each scenario, choose the appropriate test statistic based on sample size, population distribution, and whether the population standard deviation is known:

- **For large samples (typically n > 30)**:
- If the population standard deviation is known, the z-statistic is generally used.

- **For small samples (n ≤ 30)**:
- If the population is normally distributed and the standard deviation is unknown, the t-statistic is typically more appropriate.

In these scenarios, ensure that you apply these principles to determine the correct test statistic.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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