### Technology Results**Statistical Analysis Summary:**- **Pooled Proportion**: 0.34 - The pooled proportion is a weighted average of proportions from two different samples, in this case, yielding 0.34.- **Test Statistic, \( z \)**: 10.2947 - The \( z \)-value of 10.2947 indicates the number of standard deviations the test statistic is from the mean under the null hypothesis.- **Critical \( z \)**: 1.2816 - The critical \( z \)-value of 1.2816 is the threshold above which the \( z \)-value must fall to conclude that the observed effect is statistically significant at the chosen confidence level (typically 80%).- **P-value**: 0.0000 - A P-value of 0.0000 indicates very strong evidence against the null hypothesis, suggesting that the observed result is highly significant.- **80% Confidence Interval**: \[ 0.3862473 < p_1 - p_2 < 0.4822786 \] - This interval provides a range within which the true difference between proportions ( \( p_1 - p_2 \) ) lies with 80% confidence.**Statistical Hypothesis Summary:**- Null Hypothesis (\( H_0 \)): \( p_1 = p_2 \)- Alternative Hypothesis (\( H_1 \)): \( p_1 \neq p_2 \)The information displays results from a statistical test comparing two proportions. The very low P-value suggests rejecting the null hypothesis in favor of the alternative hypothesis with high confidence. Buttons:- **Print**: Initiates printing of the displayed results.- **Done**: Closes the results window.### ExplanationThe result dialog provides key statistics for interpreting a hypothesis test comparing two proportions. For an educational purpose, students and researchers can use this information to understand the strength and significance of their evidence and make informed conclusions based on the data and statistical outputs. ### Study on Virus Leak Rates of Laboratory GlovesA newspaper published an article about a study in which researchers subjected laboratory gloves to stress tests to observe virus leakage rates. Among 251 vinyl gloves tested, 55% leaked viruses. Among 251 latex gloves tested, 12% leaked viruses. The goal is to test, at a 0.10 significance level, the claim that vinyl gloves have a greater virus leak rate than latex gloves. Assume that vinyl gloves are treated as population 1.**Click the icon to view the technology results.**#### Hypothesis Testing**What are the null and alternative hypotheses?**- **Option A:** - \( H_0: p_1 < p_2 \) - \( H_1: p_1 = p_2 \)- **Option B:** - \( H_0: p_1 \neq p_2 \) - \( H_1: p_1 = p_2 \)- **Option C:** - \( H_0: p_1 > p_2 \) - \( H_1: p_1 = p_2 \)- **Option D:** - \( H_0: p_1 = p_2 \) - \( H_1: p_1 < p_2 \)- **Option E:** - \( H_0: p_1 = p_2 \) - \( H_1: p_1 > p_2 \)- **Option F:** - \( H_0: p_1 = p_2 \) - \( H_1: p_1 \neq p_2 \)**Identify the test statistic.**\[ \Box \]*(Round to two decimal places as needed.)***Identify the P-value.**\[ \Box \]*(Round to three decimal places as needed.)***Conclusion for the test:**The P-value is \[ \Underline{\hspace{30px}} \] the significance level \(\alpha\), so \[ \SelectorArrow{\hspace{30px}} \] the null hypothesis. There is \[ \SelectorArrow{\hspace{30px}} \] evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Answered: A newspaper published an article about…

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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According to a recent poll, the percentage of Americans who would vote for the incumbent president is 53%. If a random sample of 100 people in New York results in 45% who would vote for the incumbent, test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%. Use the following results and a 0.10 significance level to state your decision about H0. H0 : p=0.53 H1 : p≠0.53 test statistic: z = -1.6 p value = 0.1090
Acne is a common skin disease that affects most adolescents and can continue into adulthood. A study compared the effectiveness of three acne treatments and a placebo, all in gel form, applied twice daily for 12 weeks. The study's 517 teenage volunteers were randomly assigned to one of the four treatments. Success was assessed as clear or almost clear skin at the end of the 12 week period. The results of the study can be seen in the table below. Using the appropriate statistical test, determine if there is significant evidence that the four treatments perform differently. If so, how do they compare.
Consider a drug testing company that provides a test for marijuana usage. Among 266 tested subjects, results from 27 subjects were wrong (either a false positive or a false negative). Use a 0.10 significance level to test the claim that less than 10 percent of the test results are wrong.
One study claimed that 88 % of college students identify themselves as procrastinators. A professor believes that the claim regarding college students is too high. The professor conducts a simple random sample of 272 college students and finds that 231 of them identify themselves as procrastinators. Does this evidence support the professor's claim that fewer than 88 % of college students are procrastinators? Use a 0.02 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho p = 0.88 Ha P 0.88
Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, among 6055 patients treated with this drug, 152 developed the adverse reaction of nausea. Use a 0.01 significance level to test the claim that 3% of users develop nausea. Does nausea appear to be a problematic adverse reaction?
One study claimed that 85 % of college students identify themselves as procrastinators. A professor believes that the claim regarding college students is too high. The professor conducts a simple random sample of 108 college students and finds that 86 of them identify themselves as procrastinators. Does this evidence support the professor's claim that fewer than 85 % of college students are procrastinators? Use a 0.01 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho :p = 0.85 0.85 d: "H Answer 囲 Tables 國 Keypad Keyboard Shortcuts O > b
A large manufacturing company claims that less than 10% of its customers make a complaint about the company’s products. Test this claim at the 10% significance level, if a survey found that 29 out of a random sample of 320 of the company’s customers made a complaint about the company’s products.
Adults randomly selected for a poll were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of the subjects surveyed, 257 were in favor, 281 were opposed, and 103 were unsure. A politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin flip. Use a 0.01 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. Find the null and alternative hypothesis. H0: p=0.5 p<0.5 p≠0.5 p>0.5 H1: p<0.5 p>0.5 p≠0.5 p=0.5 If we consider + to represent those in favor, then how many of each sign is there? Positive Signs: Negative Signs: Total Signs: What is the p-value? (Round to three decimal places.) What is the conclusion about the null? What is the conclusion about the claim?

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