please use calculator method Listed below are the percent tips given when a restaurant bill contains a bad weather report on the back. At a level of alpha = 0.01, determine whether the mean percentage tip will be less than 20 percent. Assume that sigma = 2 . State hypotheses and conclusion. 18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 18.2 14.0 17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 19.4 **Some Common Values of Z\***This table lists standard Z\* values often used in statistical analyses based on various confidence levels. These values are crucial for confidence interval calculations in normally distributed data.| Confidence Level | Tail Level | Z\* ||------------------|------------|-------|| 60% | .20 | .84 || 80% | .10 | 1.28 || 90% | .05 | 1.645 || 95% | .025 | 1.96 || 96% | .02 | 2.05 || 98% | .01 | 2.33 || 99% | .005 | 2.576 |**Explanation:**- **Confidence Level**: This represents how confident we are that the true parameter lies within the interval. For example, a 95% confidence level implies that if we were to take numerous samples and create intervals, 95% of them would contain the true population parameter. - **Tail Level**: This is the area in one tail of the distribution related to the confidence level. It represents the probability that a value lies outside the desired range. - **Z\***: These are the critical Z\* values corresponding to the confidence levels. They are derived from the standard normal distribution and are used in statistical formulas for confidence intervals.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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please use calculator method

Listed below are the percent tips given when a restaurant bill contains a bad weather report on the back. At a level of alpha = 0.01, determine whether the mean percentage tip will be less than 20 percent. Assume that sigma = 2 . State hypotheses and conclusion.

18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 18.2

14.0 17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 19.4

**Some Common Values of Z\***

This table lists standard Z\* values often used in statistical analyses based on various confidence levels. These values are crucial for confidence interval calculations in normally distributed data.

| Confidence Level | Tail Level | Z\* |
|------------------|------------|-------|
| 60% | .20 | .84 |
| 80% | .10 | 1.28 |
| 90% | .05 | 1.645 |
| 95% | .025 | 1.96 |
| 96% | .02 | 2.05 |
| 98% | .01 | 2.33 |
| 99% | .005 | 2.576 |

**Explanation:**

- **Confidence Level**: This represents how confident we are that the true parameter lies within the interval. For example, a 95% confidence level implies that if we were to take numerous samples and create intervals, 95% of them would contain the true population parameter.

- **Tail Level**: This is the area in one tail of the distribution related to the confidence level. It represents the probability that a value lies outside the desired range.

- **Z\***: These are the critical Z\* values corresponding to the confidence levels. They are derived from the standard normal distribution and are used in statistical formulas for confidence intervals.

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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