**Hypothesis Testing for Proportions**A marriage counselor has traditionally observed that the proportion \( p \) of all married couples, for whom her communication program can prevent divorce, is 80%. After implementing recent changes, she claims that her program can prevent divorce in more than 80% of couples. In a random sample of 205 married couples who completed her program, 178 of them stayed together. We are tasked with determining if there is sufficient evidence to support the counselor's claim at the 0.10 level of significance.**Steps for Hypothesis Testing:**1. **State the Hypotheses:** - **Null Hypothesis (\( H_0 \))**: \( p = 0.80 \) - **Alternative Hypothesis (\( H_1 \))**: \( p > 0.80 \)2. **Determine the Type of Test Statistic:** For this scenario, we use a **z-test** to analyze population proportions.3. **Calculate the Test Statistic:** \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \] Where \( \hat{p} \) is the sample proportion, \( p_0 \) is the hypothesized population proportion (0.80), and \( n \) is the sample size (205).4. **Find the p-value:** The p-value is determined based on the calculated z-score and tells us the probability of observing a sample proportion as extreme as the one observed if the null hypothesis is true.5. **Conclusion on Evidence:** If the p-value is less than 0.10, there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, supporting the counselor's claim that the program helps more than 80% of married couples.**Note:** It's essential to carry out all intermediate calculations to at least three decimal places for accuracy. Use statistical software or z-tables to find the z-value and p-value.

(a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) E H |x E 0=0 #0

(a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) E H |x E 0=0 #0

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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p 15 Is sunscreen with an SPF 30 rating more effective at preventing sunburn than sunscreen with an SPF 15 rating? At the alpha = 0.05 level of significance, test the claim that SPF 30 sunscreen is better at preventing sunburn than 15 sunscreen. Let represent the proportion of SPF 15 sunscreen wearers who get a sunburn and represent the proportion of SPF 30 sunscreen wearers who get a sunburn. (Round your results to three decimal places) 1. Which would be correct hypotheses for this test? O O H 0 :p 15 =p 30 , H 1 :p 15 ne p 30 H 0 :p 15 =p 30 , H H 1 :p 15 <p 30 O H 0 :p 15 <p 30 ,H 1 :p 15 >p 30 O H 0 :p 15 =p 30 H 1 :p 15 >p 30 A random sample of 250 beach-goers were given SPF 15 sunscreen and asked to lay in the sun for 1 hour10 of them later reported a sunburn. Another random sample of 250 beach- goers were given SPF 30 sunscreen and asked to lay in the sun for 1 hour. 7 of them later reported a sunburn. 2.Find the test statistic 3. Give the P-value: answer only…
You may need to use the appropriate technology to answer this question. Consider the data. xi 1 2 3 4 5 yi 4 7 5 10 14 Use the t test to test the following hypotheses (? = 0.05): H0: β1 = 0 Ha: β1 ≠ 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format. Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.) Sourceof Variation Sumof Squares Degreesof Freedom MeanSquare F p-value Regression Error Total Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value =
CHALLENGE ACTIVITY 402562.2600368.qx3zqy7 8.2.3: Hypothesis testing for two population proportions (one-tailed z-test). Jump to level 1 A university department chair believes that the afternoon section of a large survey class has a consistently lower proportion of students that pass the class compared to the morning section. The chair checks a random sample of student records from each section. The results of the data collected are shown below. Morning section Afternoon section Successes Observations p-hat_1 346 Successes 400 Observations 0.865 p-hat_2 Confidence level 95% -0.5548 p-value 0.2912 3 2 6 2 P= Ex 1.234 Morning section samples: ₁ Ex: 9 Afternoon section samples: 1₂ Sample proportion for morning section samples: p1 Sample proportion for afternoon section samples: p₂ – O 500 LE E 2 № 7 || ||| Ex: 1.234 D D DO
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Consider the data. xi 3 12 6 20 14 yi 60 40 65 5 15 Use the t test to test the following hypotheses (? = 0.05): H0: ?1 = 0 Ha: ?1 ≠ 0 Find the value of the test statistic. (Round your answer to three decimal places.) Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.
Psyc 10 Laboratory Assignment 3 - Chapt 4 & 5 Application #2 Stressed Much More? O To test the effectiveness of a new stress reduction method: 20 randomly selected people are trained in the stress reduction method and measured. Their mean stress level is 25. O In the general population, it is known that stress levels are: u = 40 and o=10. O Does the new stress reduction method lower stress? O Using the five steps of hypothesis testing, answer the question above. O Significance level?
H1: This is a homework question. I chose a Null Hypothesis that is equal to the Alternative because the professor is comparing the two formats. Is my reasoning correct? Would this be a directional question? A statistics professor is interested in finding out whether students perform better on exams if they are conducted in the classroom or online. He compares the final exam scores of his online statistics class with the exam scores of his in-person class. What is the null hypothesis for this scenario? Null Hypothesis: final exam scores in class = final exam scores online Alternative Hypothesis: final exam scores in class is NOT Equal to final exam scores online
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Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H0: p=0.2 versus H1: p>0.2 n=250; x=55, α=0.1