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

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Author: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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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