The standard deviation for all medium size hot dogs is 49.99 calories. A random selection of 55 different brands of medium size hot dogs has a mean of 239 calories. Comfort Food Magazine states the mean calories of a medium size hot dog size is 233. Is there sufficient evidence to conclude that the mean calories of a medium size hot dog is 233 based on level of significance of 0.03? ### Transcription and Explanation#### Finding Critical Values (CV)- **Question**: To find our Critical Value(s) (CV), will we use invNorm(), invT()? - **Options**: - Dropdown menu option: `invNorm()`#### Explanation- **Question**: Please explain the reason for the correct answer for step c. - **Answer**: The population standard deviation is given (σ).#### Calculation- **Instruction**: Round to Two Decimal Places - **CV1**: [Input Box] - **CV2**: [Input Box]#### Formula Selection- **Question**: What formula will we use for the test value? - **Options**: 1. $ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} $ 2. $ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} $ 3. $ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} $ *(This option is selected)* 4. $ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p}(1 - \hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}} $This content is structured to guide students in selecting the appropriate tool and formula for statistical calculations based on given conditions, particularly when the population standard deviation is provided. **Title: Statistical Analysis: Calculating Test Values****Instructions:****Step g**: Determine the values for each part of our test value formula. Once completed, use this information to calculate the test value.1. **Round to the Nearest Whole Number:** - $ \bar{x} $ (Sample Mean): ___ - $ \mu $ (Population Mean): ___ *(Note: Assume $ H_0 $ (the null hypothesis) is true until there is evidence against it.)*2. **Round to Two Decimal Places:** - $ \sigma $ (Standard Deviation): ___3. **Sample Size:** - $ n $ (Sample size): ___4. **Round to Two Decimal Places:** - $ z $ (Z-score): ___**Step h**: Choose the option that best represents where the test value will be situated on the appropriate normal distribution curve.- **Left-Tail Test** This section emphasizes calculating components of the test value and understanding their placement in statistical analysis.

Name: The standard deviation for all medium size hot dogs is 49.99 calories.
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Description: The standard deviation for all medium size hot dogs is 49.99 calories. A random selection of 55 different brands of medium size hot dogs has a mean of 239 calories. Comfort Food Magazine states the mean calories of a medium size hot dog size is 233.

c) To find our critical value(s) (cv) we will use invNorm(), invT() ? Answer: invNorm() d) The population standard deviation is given (σ) To find critical values: The critical value of z is obtained Ti 83 calculator function “=invNorm(Probability, mean, standard deviation)”. Output obtained from Ti 83 calculator is given below: From the output, the critical value CV1 is -2.17 The critical value CV2 is 2.17 f) The formula for the test value is z=x-μσng) Values of each component for test value formula: x=239μ=233σ=49.99n=55 The test statistic will be obtained as below: z=239-23349.9955 =66.7407 =0.89 Thus, the test statistic z is 0.89

Answered: c) To find our Critical Value(s) (CV),…

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The standard deviation for all medium size hot dogs is 49.99 calories. A random selection of 55 different brands of medium size hot dogs has a mean of 239 calories. Comfort Food Magazine states the mean calories of a medium size hot dog size is 233. Is there sufficient evidence to conclude that the mean calories of a medium size hot dog is 233 based on level of significance of 0.03?

**Title: Statistical Analysis: Calculating Test Values**

**Instructions:**

**Step g**: Determine the values for each part of our test value formula. Once completed, use this information to calculate the test value.

1. **Round to the Nearest Whole Number:**
- $ \bar{x} $ (Sample Mean): ___
- $ \mu $ (Population Mean): ___

*(Note: Assume $ H_0 $ (the null hypothesis) is true until there is evidence against it.)*

2. **Round to Two Decimal Places:**
- $ \sigma $ (Standard Deviation): ___

3. **Sample Size:**
- $ n $ (Sample size): ___

4. **Round to Two Decimal Places:**
- $ z $ (Z-score): ___

**Step h**: Choose the option that best represents where the test value will be situated on the appropriate normal distribution curve.

- **Left-Tail Test**

This section emphasizes calculating components of the test value and understanding their placement in statistical analysis.

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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c) To find our Critical Value(s) (CV), will we use invNorm(), invT()? invNorm() d) Please explain the reason for the correct answer for step c. The population standard deviation is given (a). Round to Two Decimal Places CV1 = CV2 = f) What formula will we use for the test value?