Given the accompanying sample data, use Excel’s formula options to determine if the population mean is greater than 116 at the 5% significance level. Assume that the population is normally distributed. **Hypothesis Test for the Population Mean When σ is Unknown**Given the accompanying sample data, use Excel’s formula options to determine if the population mean is greater than 116 at the 5% significance level. Assume that the population is normally distributed.**Instructions:**- Complete the following analysis. Do not hard code values in your calculations. Use cells E9 through E12 and A1:A20 to compute the values.**Hypotheses:**- $ H_0: \mu \leq 116 $- $ H_a: \mu > 116 $**Parameters:**- $ \alpha = 0.05 $- $ n = 20 $**Calculations:**- **Sample Mean:** Calculate using values in cells A1 through A20. - **Standard Deviation:** Calculate using values in cells A1 through A20.- **t-test Statistic:** Calculate using cells E9, E10, E11, E12, E14, and E16.- **p-value:** Compute the probability that t is greater than the t-test statistic.**Conclusion:**- If the p-value is > 0.05, do not reject $ H_0 $. At the 5% significance level, the population mean is less than or equal to 116.- If the p-value is < 0.05, reject $ H_0 $. At the 5% significance level, the population mean is greater than 116.Ensure accuracy by strictly using the specified cells for calculations.

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Description: Given the accompanying sample data, use Excel’s formula options to determine if the population mean is greater than 116 at the 5% significance level. Assume that the population is normally distributed. **Hypothesis Test for the Population Mean When σ

Enter the given data in excel as shown below. Also Use the following formula to get the sample mean,…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Given the accompanying sample data, use Excel’s formula options to determine if the population mean is greater than 116 at the 5% significance level. Assume that the population is normally distributed.

**Hypothesis Test for the Population Mean When σ is Unknown**

Given the accompanying sample data, use Excel’s formula options to determine if the population mean is greater than 116 at the 5% significance level. Assume that the population is normally distributed.

**Instructions:**

- Complete the following analysis. Do not hard code values in your calculations. Use cells E9 through E12 and A1:A20 to compute the values.

**Hypotheses:**

- $ H_0: \mu \leq 116 $
- $ H_a: \mu > 116 $

**Parameters:**

- $ \alpha = 0.05 $
- $ n = 20 $

**Calculations:**

- **Sample Mean:** Calculate using values in cells A1 through A20.

- **Standard Deviation:** Calculate using values in cells A1 through A20.

- **t-test Statistic:** Calculate using cells E9, E10, E11, E12, E14, and E16.

- **p-value:** Compute the probability that t is greater than the t-test statistic.

**Conclusion:**

- If the p-value is > 0.05, do not reject $ H_0 $. At the 5% significance level, the population mean is less than or equal to 116.
- If the p-value is < 0.05, reject $ H_0 $. At the 5% significance level, the population mean is greater than 116.

Ensure accuracy by strictly using the specified cells for calculations.

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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