H0: p, μ, or σ | =, >, <, or ≠ ________________ H1:p, μ, or σ | =, >, <, or ≠ ________________ Identify the test statistic ______________ (Round to two decimal palces as needed.) Identify the P-value ____________________ (Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addres the original claim. Reject or Fail to Reject the null hypothesis. There is or is not sufficient evidence at the 0.05 significance level to warrant rejecion of or reject the claim that the sample is from a population with a mean equal to 8.953 g. A data set includes weights (in grams) of 40 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 40 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 0.10 significance level.Click the icon to view the Statdisk display.---Identify the null and alternative hypotheses.H₀: [dropdown] [input box]H₁: [dropdown] [input box](Type integers or decimals. Do not round.) **Hypothesis Testing using t Test**In the analysis of statistical data, hypothesis testing is a method used to determine if there is enough evidence to reject a null hypothesis. This example illustrates a t Test result from a statistical software.**Null and Alternative Hypotheses:**The image provides areas for entering the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\).**Statdisk Display:**The software output, shown in the Statdisk Display window, summarizes the results of a t Test:- **Test Statistic, t:** \(-3.63705\) - This value indicates the calculated t-value from the sample data.- **Critical t:** \(\pm 1.68488\) - This represents the critical t-value at a chosen significance level, which defines the cutoff points for rejecting the null hypothesis.- **P-value:** \(0.00080\) - A P-value is the probability of observing the test results under the null hypothesis. A low P-value (typically ≤ 0.05) suggests that the null hypothesis may be rejected in favor of the alternative hypothesis.**Conclusion:**Since the P-value is considerably lower than typical significance levels (e.g., 0.05), this suggests strong evidence against the null hypothesis, leading to its possible rejection in favor of the alternative hypothesis.

Given: n = 40 μ = 8.953 α = 0.10

Answered: H0: p, μ, or σ | =, >, <, or ≠…

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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H0: p, μ, or σ | =, >, <, or ≠ ________________

H1:p, μ, or σ | =, >, <, or ≠ ________________

Identify the test statistic ______________ (Round to two decimal palces as needed.)

Identify the P-value ____________________ (Round to three decimal places as needed.)

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

Reject or Fail to Reject the null hypothesis. There is or is not sufficient evidence at the 0.05 significance level to warrant rejecion of or reject the claim that the sample is from a population with a mean equal to 8.953 g.

A data set includes weights (in grams) of 40 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 40 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 0.10 significance level.

Click the icon to view the Statdisk display.

---

Identify the null and alternative hypotheses.

H₀: [dropdown] [input box]

H₁: [dropdown] [input box]

(Type integers or decimals. Do not round.)

**Hypothesis Testing using t Test**

In the analysis of statistical data, hypothesis testing is a method used to determine if there is enough evidence to reject a null hypothesis. This example illustrates a t Test result from a statistical software.

**Null and Alternative Hypotheses:**

The image provides areas for entering the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\).

**Statdisk Display:**

The software output, shown in the Statdisk Display window, summarizes the results of a t Test:

- **Test Statistic, t:** \(-3.63705\)
- This value indicates the calculated t-value from the sample data.

- **Critical t:** \(\pm 1.68488\)
- This represents the critical t-value at a chosen significance level, which defines the cutoff points for rejecting the null hypothesis.

- **P-value:** \(0.00080\)
- A P-value is the probability of observing the test results under the null hypothesis. A low P-value (typically ≤ 0.05) suggests that the null hypothesis may be rejected in favor of the alternative hypothesis.

**Conclusion:**
Since the P-value is considerably lower than typical significance levels (e.g., 0.05), this suggests strong evidence against the null hypothesis, leading to its possible rejection in favor of the alternative hypothesis.

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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