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Hello I just need help with the test statistic, the p-value, and where the test point lies on the distribution. Thank you :)

Hello I just need help with the test statistic, the p-value, and where the test point lies on the distribution. Thank you :)

MATLAB: An Introduction with Applications
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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Hello I just need help with the test statistic, the p-value, and where the test point lies on the distribution. Thank you :)

 

**Step-by-Step Hypothesis Testing Guide** **d. Calculate the value of the test statistic.** 1. **Determine the test statistic value** based on your sample data and the hypothesis test formula applicable (e.g., z-test or t-test). **What is the value of the p-value? Illustrate the p-value on the graph in step 3.** 2. **Calculate the p-value** using statistical software or tables corresponding to your test statistic value. **e. Plot the statistic on the graph of the distribution. In which region does the test point lie?** 3. **Illustrate the test statistic on a distribution curve** (normal or t-distribution). - Identify the region where the test statistic falls, relative to the critical region defined by your significance level (alpha). **Fill in the blanks. In the second blank fill in the appropriate sign: > or ≤.** 4. **State the comparison**: - p-value = _____________ ___________ 0.05 = α **f. Select the proper decision about the null hypothesis.** 5. **Decide on the null hypothesis (Ho)**: - Reject Ho - Fail to Reject Ho **g. Interpret the decision in terms of the alternative hypothesis.** 6. **Contextualize your decision**: - If you reject Ho, conclude that there is sufficient evidence to support the alternative hypothesis. - If you fail to reject Ho, note that there is not enough evidence to support the alternative hypothesis. By following these steps, students can adequately perform hypothesis testing and interpret the results in standard statistical terms.
Transcribed Image Text:**Step-by-Step Hypothesis Testing Guide** **d. Calculate the value of the test statistic.** 1. **Determine the test statistic value** based on your sample data and the hypothesis test formula applicable (e.g., z-test or t-test). **What is the value of the p-value? Illustrate the p-value on the graph in step 3.** 2. **Calculate the p-value** using statistical software or tables corresponding to your test statistic value. **e. Plot the statistic on the graph of the distribution. In which region does the test point lie?** 3. **Illustrate the test statistic on a distribution curve** (normal or t-distribution). - Identify the region where the test statistic falls, relative to the critical region defined by your significance level (alpha). **Fill in the blanks. In the second blank fill in the appropriate sign: > or ≤.** 4. **State the comparison**: - p-value = _____________ ___________ 0.05 = α **f. Select the proper decision about the null hypothesis.** 5. **Decide on the null hypothesis (Ho)**: - Reject Ho - Fail to Reject Ho **g. Interpret the decision in terms of the alternative hypothesis.** 6. **Contextualize your decision**: - If you reject Ho, conclude that there is sufficient evidence to support the alternative hypothesis. - If you fail to reject Ho, note that there is not enough evidence to support the alternative hypothesis. By following these steps, students can adequately perform hypothesis testing and interpret the results in standard statistical terms.
**Math 2 - Statistics** **Class Participation 20** **Chapter 22** A researcher wants to investigate the claim that more than 70% of Americans take prescription drugs. The researcher randomly selects 225 Americans and finds that 170 do take at least one prescribed drug. Test the claim at the 5% significance level. 1. **State the null and the alternative hypothesis using the proper notation established in class.** - Null Hypothesis (H₀): p ≤ 0.70 - Alternative Hypothesis (Hₐ): p > 0.70 2. **Is the sample random?** - **Answer:** YES 3. **Calculate:** - np₀ = 157.5 - n(1 - p₀) = 67.5 Are np₀ ≥ 10 and n(1 - p₀) ≥ 10? - **Answer:** YES 4. **Is the sample size less than 10% of the population size?** - **Answer:** NO 5. **Have the conditions of the test been satisfied? (For the purpose of this class exercise, continue with the test even if the conditions are not satisfied.)** - **Answer:** YES 6. **What is the significance level (α)?** - **Answer:** 5% (0.05) 7. **What is the value(s) of the critical value(s)? Look this value up on a table!** - **Answer:** z₀.₀₅ = 1.962 **Diagram:** The image includes a bell curve, which is a graphical representation of a normal distribution. The curve is centered around zero and extends equally in both directions. The critical value, z₀.₀₅ = 1.962, is labeled on the positive side of the curve, indicating the cutoff for a right-tailed test at a 5% significance level.
Transcribed Image Text:**Math 2 - Statistics** **Class Participation 20** **Chapter 22** A researcher wants to investigate the claim that more than 70% of Americans take prescription drugs. The researcher randomly selects 225 Americans and finds that 170 do take at least one prescribed drug. Test the claim at the 5% significance level. 1. **State the null and the alternative hypothesis using the proper notation established in class.** - Null Hypothesis (H₀): p ≤ 0.70 - Alternative Hypothesis (Hₐ): p > 0.70 2. **Is the sample random?** - **Answer:** YES 3. **Calculate:** - np₀ = 157.5 - n(1 - p₀) = 67.5 Are np₀ ≥ 10 and n(1 - p₀) ≥ 10? - **Answer:** YES 4. **Is the sample size less than 10% of the population size?** - **Answer:** NO 5. **Have the conditions of the test been satisfied? (For the purpose of this class exercise, continue with the test even if the conditions are not satisfied.)** - **Answer:** YES 6. **What is the significance level (α)?** - **Answer:** 5% (0.05) 7. **What is the value(s) of the critical value(s)? Look this value up on a table!** - **Answer:** z₀.₀₅ = 1.962 **Diagram:** The image includes a bell curve, which is a graphical representation of a normal distribution. The curve is centered around zero and extends equally in both directions. The critical value, z₀.₀₅ = 1.962, is labeled on the positive side of the curve, indicating the cutoff for a right-tailed test at a 5% significance level.
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