Answered: A data set includes weights (in grams)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A data set includes weights (in grams) of 33 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 33 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. Test the given claim by using the display provided from Statdisk. Use a 0.05 significance level.

**Identify the null and alternative hypotheses.**

- \( H_0: \) [Dropdown for choosing mathematical signs: =, <, >] [Box for entering value]
- \( H_1: \) [Dropdown for choosing mathematical signs: =, <, >] [Box for entering value]

*(Type integers or decimals. Do not round.)*

**Identify the test statistic.**

- [Box for entering the test statistic value]

*(Round to two decimal places as needed.)*

**Identify the P-value.**

- [Box for entering the P-value]

*(Round to three decimal places as needed.)*

**State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.**

- [Dropdown: Reject/Fail to reject] the null hypothesis. There [Dropdown: is/is not] sufficient evidence at the 0.10 significance level to [Dropdown: support/refute] the claim that the sample is from a population with a mean systolic blood pressure level greater than 120 mm Hg.

### Educational Website Content: Statistical Analysis of Reese's Peanut Butter Cup Miniatures

A data set includes weights (in grams) of 33 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 33 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. Test the given claim by using the display provided from Statdisk, using a 0.05 significance level.

#### Steps for Analysis:

1. **Identify the null and alternative hypotheses:**
- \( H_0: \) The population mean is equal to 8.953 g.
- \( H_1: \) The population mean is not equal to 8.953 g.

2. **Statistical Test Information:**
- **Test Type:** t Test
- **Test Statistic, t:** -3.89274
- **Critical t:** ±2.03693
- **P-value:** 0.00047

#### Interpretation:

- **Null Hypothesis (\( H_0 \)):** The assumption that the sample comes from a population with a mean weight equal to 8.953 grams.

- **Alternative Hypothesis (\( H_1 \)):** The assumption that the sample comes from a population with a mean weight not equal to 8.953 grams.

- **Test Statistic:** A t-value of -3.89274 was calculated, which measures the difference between the sample mean and the population mean in terms of standard deviation units.

- **Critical t-value:** The threshold values (±2.03693) determine the boundaries for rejecting the null hypothesis at the 0.05 significance level.

- **P-value:** With a p-value of 0.00047, which is less than the significance level of 0.05, the null hypothesis is rejected, indicating that the sample mean is significantly different from the population mean.

#### Conclusion:
Given the test results, there is strong evidence to reject the null hypothesis. Therefore, it is likely that the sample comes from a population with a mean weight that is not equal to 8.953 grams.

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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