Follow PHANTOMS acronym ---### Steps to Conducting a Statistical Test**P - Parameter Statement**Define the parameter of interest in the context of the problem.**H - Hypotheses**State the null and alternative hypotheses clearly. The null hypothesis (H₀) typically represents a statement of no effect or no difference, while the alternative hypothesis (H₁ or Ha) represents a statement of an effect or difference.**A - Assumptions & Conditions**List and check the assumptions and conditions necessary for conducting the test. This might include assumptions about the distribution of the data, sample size, independence, etc.**N - Name the Test**Identify and name the appropriate statistical test you will use based on the parameter and the hypotheses.**T - Test Statistic**Calculate the test statistic using the sample data. The test statistic is a standardized value that is calculated from sample data during a hypothesis test.**O - Obtain the P-Value**Find the p-value associated with the test statistic. The p-value indicates the probability of observing your data, or something more extreme, if the null hypothesis is true.**M - Make a Decision about the Null Hypothesis**Compare the p-value to the significance level (α) to make a decision about the null hypothesis. If p-value ≤ α, reject the null hypothesis; if p-value > α, fail to reject the null hypothesis.**S - State Your Conclusion About the Claim**Provide a conclusion in the context of the original claim. Interpret the results of your hypothesis test in plain language, explaining what the decision implies about the context of the problem.--- **Problem Statement: Testing the Average Number of Gum Sticks Chewed Per Day**A recent study stated that if a person chewed gum, the average number of sticks of gum he or she chewed daily was 8. To test this claim, a researcher selected a random sample of 36 gum chewers and found the mean number of sticks of gum chewed per day was 9. The standard deviation of the sample was 1. Use the level of significance $ \alpha = 0.05 $ to test the claim that the number of sticks of gum a person chews per day is actually greater than 8. Use any method, however, follow the PHANTOMS acronym to answer the question.**PHANTOMS Acronym for Hypothesis Testing:**1. **P:** Parameter of interest - The mean number of sticks of gum chewed per day.2. **H:** Hypotheses – - Null hypothesis ($ H_0 $): $ \mu = 8 $ - Alternative hypothesis ($ H_a $): $ \mu > 8 $3. **A:** Assumptions - The sample data are random, the sample size is large enough (n=36), and the population is normally distributed or the sample size is sufficiently large for the Central Limit Theorem to apply.4. **N:** Name the procedure - One-sample t-test for the mean.5. **T:** Test statistic – Calculate the test statistic using the formula:\[ t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}} \] Where: - $ \bar{x} = 9 $ (sample mean) - $ \mu_0 = 8 $ (population mean under the null hypothesis) - $ s = 1 $ (sample standard deviation) - $ n = 36 $ (sample size) \[ t = \frac{9 - 8}{1 / \sqrt{36}} = \frac{9 - 8}{1 / 6} = \frac{1}{1 / 6} = 6 \] 6. **O:** Obtain the p-value – Using a t-distribution table or calculator, find the p-value for the test statistic $ t = 6 $ with $ df = n - 1 = 35 $.7. **M

Given Level of significance=alpha=0.05, n=36 and Xbar=9, s=1 We want to test H1:mu>8

A recent study stated that if a person chewed gum, the average number of sticks of gum he or she chewed daily was 8. To test the claim, a researcher selected a random sample of 36 gum chewers and found the mean number of sticks of gum chewed per day was 9. The standard deviation of the sample was 1. Use the level of significance of 0.05 , test the claim that the number of sticks of gum a person chews per day is actually greater than 8? Use any method, however, follow the PHANTOMS acronym to answer the question.

A recent study stated that if a person chewed gum, the average number of sticks of gum he or she chewed daily was 8. To test the claim, a researcher selected a random sample of 36 gum chewers and found the mean number of sticks of gum chewed per day was 9. The standard deviation of the sample was 1. Use the level of significance of 0.05 , test the claim that the number of sticks of gum a person chews per day is actually greater than 8? Use any method, however, follow the PHANTOMS acronym to answer the question.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: えもて to

Q: Help!!! Please answer all correctly

A: However, I can provide you with general guidance on color mixing principles and how to approach…

Q: Explain Bonferroni correction?

A: Bonferroni Correction- It is multiple-comparison correction. If you want to do statistical test for…

Q: art b is wrong

A: The mean and standard deviation for difference is 12.35 and 59.89 respectively.

Q: (1) Consider the plots of various functions, f(x), below. We can say for certain that one could not…

A: Let X be a continuous random variable that has the probability density function fx. Then, the…

Q: they ask about hours will be 3h?

Q: part c is wrong. please fix that!!

A: s=23.90 n=16

Q: part c is not correct i

A: The given table represents the security analyst’s expected return on two stocks and the market index…

Q: Evaluate ſ(r -)dr.

Q: 6. arctan 1 3

Q: a-e please as well!

A: As per the guidelines we are supposed to solve only the first 3 subparts. Please repost the other…

Q: Find e

Q: what is the exact answer for gave

A: Given that,gt=51+t2We need to compute the average value gave of the function on the interval 0,7.

Q: Ex²– 1) x = [1,2,3,4,5] QUESTION 2 x-[1,2,3,4,5]|

A: Solution: 1. The given data is

Concept explainers

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus.

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.

Question

Follow PHANTOMS acronym

---

### Steps to Conducting a Statistical Test

**P - Parameter Statement**
Define the parameter of interest in the context of the problem.

**H - Hypotheses**
State the null and alternative hypotheses clearly. The null hypothesis (H₀) typically represents a statement of no effect or no difference, while the alternative hypothesis (H₁ or Ha) represents a statement of an effect or difference.

**A - Assumptions & Conditions**
List and check the assumptions and conditions necessary for conducting the test. This might include assumptions about the distribution of the data, sample size, independence, etc.

**N - Name the Test**
Identify and name the appropriate statistical test you will use based on the parameter and the hypotheses.

**T - Test Statistic**
Calculate the test statistic using the sample data. The test statistic is a standardized value that is calculated from sample data during a hypothesis test.

**O - Obtain the P-Value**
Find the p-value associated with the test statistic. The p-value indicates the probability of observing your data, or something more extreme, if the null hypothesis is true.

**M - Make a Decision about the Null Hypothesis**
Compare the p-value to the significance level (α) to make a decision about the null hypothesis. If p-value ≤ α, reject the null hypothesis; if p-value > α, fail to reject the null hypothesis.

**S - State Your Conclusion About the Claim**
Provide a conclusion in the context of the original claim. Interpret the results of your hypothesis test in plain language, explaining what the decision implies about the context of the problem.

---

**Problem Statement: Testing the Average Number of Gum Sticks Chewed Per Day**

A recent study stated that if a person chewed gum, the average number of sticks of gum he or she chewed daily was 8. To test this claim, a researcher selected a random sample of 36 gum chewers and found the mean number of sticks of gum chewed per day was 9. The standard deviation of the sample was 1.

Use the level of significance $ \alpha = 0.05 $ to test the claim that the number of sticks of gum a person chews per day is actually greater than 8. Use any method, however, follow the PHANTOMS acronym to answer the question.

**PHANTOMS Acronym for Hypothesis Testing:**
1. **P:** Parameter of interest - The mean number of sticks of gum chewed per day.
2. **H:** Hypotheses –
- Null hypothesis ($ H_0 $): $ \mu = 8 $
- Alternative hypothesis ($ H_a $): $ \mu > 8 $
3. **A:** Assumptions - The sample data are random, the sample size is large enough (n=36), and the population is normally distributed or the sample size is sufficiently large for the Central Limit Theorem to apply.
4. **N:** Name the procedure - One-sample t-test for the mean.
5. **T:** Test statistic – Calculate the test statistic using the formula:
\[ t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}} \]
Where:
- $ \bar{x} = 9 $ (sample mean)
- $ \mu_0 = 8 $ (population mean under the null hypothesis)
- $ s = 1 $ (sample standard deviation)
- $ n = 36 $ (sample size)
\[ t = \frac{9 - 8}{1 / \sqrt{36}} = \frac{9 - 8}{1 / 6} = \frac{1}{1 / 6} = 6 \]

6. **O:** Obtain the p-value – Using a t-distribution table or calculator, find the p-value for the test statistic $ t = 6 $ with $ df = n - 1 = 35 $.
7. **M

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Exponents$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

ho participate in volunteer activities.
It showed incorrect
C. 0.4638. O d. 0.1587 O e. Cannot be determined
is this usual or unusual
(can you show step by step the excel or PHstat method to use to solve question a and b? 1.According to a report from a business intelligence company, smartphone owners are using an average of 17 apps per month. Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is 3. a).If you select a random sample of 16 smartphone owners, what is the probability that the sample mean is between 16.5 and 17.5? b). If you select a random sample of 16 smartphone owners, what is the probability that the sample mean is between 16 and 17?
sh 28 (40,14) सिक्री SE
Standard Dev. S= Σ (4-6.27² 3-1