The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 49 drivers over the age of 60 and finds that the mean number of miles per day driven is 22.8. The population standard deviation is 3.5 miles. At a=0.05, is there sufficient evidence that those drivers over 60 years old drive less on average than 24 miles per day? ### Statistical Testing Formula SelectionThis section guides users in selecting the appropriate formula for calculating test values in statistical analyses.**Critical Value (CV) Selection:**- Function: `invNorm`- Round the result to two decimal places.- CV Input Box: For manual entry of the calculated critical value.---**Question: Which formula will we use for the test value?**1. **Option 1:** \[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \]2. **Option 2:** \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \] - **Selected Option:** This option is chosen, indicating it is suitable for the current test context, often used for finding the z-score when population standard deviation is known.3. **Option 3:** \[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \]4. **Option 4:** \[ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]5. **Option 5:** \[ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} \]- **Notes:** - The symbol $\bar{x}$ represents the sample mean. - The symbol $\mu$ represents the population mean. - The symbol $\sigma$ represents the population standard deviation. - The symbol $s$ represents the sample standard deviation. - $\hat{p}$ and $\hat{q}$ are sample proportions. - $n$ refers to the sample size.A check mark indicates the confirmation of selected option two for this test.

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Description: The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 49 drivers over the age of 60 and finds that the mean number of miles per day

GIVEN: n=49 Population mean μ=24population standard deviation σ=3.5sample mean x=22.8α=0.05…

Answered: The average number of miles a person…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 49 drivers over the age of 60 and finds that the mean number of miles per day driven is 22.8. The population standard deviation is 3.5 miles. At a=0.05, is there sufficient evidence that those drivers over 60 years old drive less on average than 24 miles per day?

### Statistical Testing Formula Selection

This section guides users in selecting the appropriate formula for calculating test values in statistical analyses.

**Critical Value (CV) Selection:**
- Function: `invNorm`
- Round the result to two decimal places.
- CV Input Box: For manual entry of the calculated critical value.

---

**Question: Which formula will we use for the test value?**

1. **Option 1:**
\[
z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}}
\]

2. **Option 2:**
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
- **Selected Option:** This option is chosen, indicating it is suitable for the current test context, often used for finding the z-score when population standard deviation is known.

3. **Option 3:**
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]

4. **Option 4:**
\[
t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
\]

5. **Option 5:**
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}}
\]

- **Notes:**
- The symbol $\bar{x}$ represents the sample mean.
- The symbol $\mu$ represents the population mean.
- The symbol $\sigma$ represents the population standard deviation.
- The symbol $s$ represents the sample standard deviation.
- $\hat{p}$ and $\hat{q}$ are sample proportions.
- $n$ refers to the sample size.

A check mark indicates the confirmation of selected option two for this test.

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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