= (Enter 3 decimal places) z = (Round to 2 decimal places) P-value = (Enter at least 4 decimal places)
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In recent years, approximately 55% of eligible voters take the time to vote in presidential elections. A poll based on a random sample of 200 eligible voters finds that 128 plan to vote in the next presidential election.
Does this data provide convincing evidence at the ?α = 0.05 level that the proportion of eligible voters who will take time to vote in the next presidential election differs from 0.55?
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- The National Academy of Science reported that 41% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 41%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 186 recent articles published by reputable mathematics research journals and finds that 92 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 41%? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. circle the answer below. H0 p=0.41 ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.41 A.<B.≠C.> Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places Step 3 of 3: Draw a conclusion and interpret the decision. A. We reject the null hypothesis and conclude that there is insufficient evidence at a…Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 33arrests last month, 25were of males aged 15 to 34 years. Use a 1%level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. a. What is the level of significance? answer .01 b.State the null and alternate hypotheses. Which one? Its the third. H0: p< 0 .7; H1: p= 0.7 H0: p≠0.7; H1: p= 0.7 H0: p= 0.7; H1: p≠0.7 H0: p= 0 .7; H1: p< 0.7 H0: p= 0.7; H1: p> 0.7 c. What sampling distribution will you use? Its the last one. The Student's t, since np> 5 and…The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.2% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.6% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 9.2% in the general adult American population. Test the relevant hypotheses using a 10% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) Ho: P H₁: p b. Based on the hypotheses, find the following: c. Test Statistic = 8.016 X 0° 0.092 d. p-value = 0 0.092 e. Based on the above we choose to Reject the null hypothesis OB OT f. The correct summary would be: There is enough evidence to support the claim o that the true…
- In a survey of 1000 adult Americans, 45.7% indicated that they were somewhat interested or very interested in having web access in their cars. Suppose that the marketing manager of a car manufacturer claims that the 45.7% is based only on a sample and that 45.7% is close to half, so there is no reason to believe that the proportion of all adult Americans who want car web access is less than 0.50. Is the marketing manager correct in his claim? Provide statistical evidence to support your answer. For purposes of this exercise, assume that the sample can be considered as representative of adult Americans. Test the relevant hypotheses using ? = 0.05. Find the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z= P-value= chose the conclusion in the context of the problem. a) Reject H0. We do not have convincing evidence that the proportion of all adult Americans who want car web access is less than 0.5. The marketing…The National Institute of Mental Health published an article stating that in any one-year period, approximately 8.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.3% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.8% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? H0: H1: b.) Based on the hypotheses, find the following: c.) Test Statistic = d.) p-value = e.) Based on the above we choose to________________ f.) The correct summary would be:____________ that the true proportion of people in that city suffering from depression or a depressive illness is more than the percent in the general…You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 50% at a level of significance of a = 0.10. According to your sample, 49 out of 92 potential voters prefer the Democratic candidate.
- Management of a theater in a large city wants to know whether its popularity increased after it ran a popular musical. According to a previous study, 25% of city residents said they had been to the theater in the past year. A more recent study, conducted after the musical had run for a year, found that 156 of 536 residents sampled said they had been to the theater in the past year. Is there evidence at the ? = 0.05 level that the number of residents who have been to the theater has increased in the last year?In 2001, the polls found that 81% of American adults believed that there was a conspiracy in the death of President Kennedy. Assume a recent poll asked 1160 American adults if they believe there was a conspiracy in the assassination and it found that 897 believe there was a conspiracy. Does the data show that the proportion of Americans who believe in this conspiracy is now lower? Test at the 9% level. What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? Fill in the correct null and alternative hypotheses:A 2012 survey of 417 American adults indicates that 15% of cell phone owners do their browsing on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38% of Chinese mobile web users only access the internet through their cell phones. We wish to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is less than the Chinese proportion of 38%. (a) The Null Hypothesis, in mathematical symbols, is: H0: p = ______ (b) The Alternative Hypothesis, in mathematical symbols, is: HA : p = _______ In both the null and alternative hypotheses, the symbol ( p ) is the proportion of American adult cell phone owners who do their browsing on their phone. (c) The standard error based on the null hypothesis is... :________ (d) Our data indicates a proportion of Americans who use their phones to browse is…
- An educator believes that the proportion of finance majors seeking to earn an MBA degree equals the proportion of management majors seeking to earn an MBA degree in the population. A random sample of 100 finance majors is taken and 24 indicate that they will seek to earn an MBA degree. Likewise, a random sample of 400 management majors is taken and 65 indicate that they will seek to earn an MBA degree. Using this information, test the educator’s claim at the 0.05 levelXu and Garcia (2008)conducted a research study demonstrating that 8-month-old infants appear to recognize which samples are likely to be obtained from a population and which are not. In the study, the infants watched as a sample of n = 5 ping-pong balls was selected from a large box. In one condition, the sample consisted of 1 red ball and 4 white balls. After the sample was selected, the front panel of the box was removed to reveal the contents. In the expected condition, the box contained primarily white balls like the sample, and the infants looked at it for an average of M = 7.5 seconds. In the unexpected condition, the box had primarily red balls, unlike the sample, and the infants looked at it for M = 9.9. The researchers interpreted the results as demonstrating that the infants found the unexpected result surprising and, therefore, more interesting than the expected result. Assuming that the standard error for both means is σM = 1 second, draw a bar graph showing the two sample…A demographer wants to know what proportion of women in different countries dye their hair. They take a random sample of women from Korea and another random sample of women from China. In Korea, 47% dyed their hair. In China, 56% dyed their hair. (a) What hypotheses would the demographer use to test if women in China are more likely to dye their hair than women in Korea? H0: pChina=pKorea vs. Ha: pChina ≠ pKoreaH0: pChina - pKorea = 0 vs. Ha: pChina - pKorea > 0 H0: μChina-μKorea = 0 vs. Ha: μChina-μKorea ≠ 0H0: pChina-pKorea = 0.09 vs. Ha: pChina-pKorea ≠ 0.09H0: μChina = 0.56 vs. Ha: μKorea = 0.47 (b) Suppose their test yielded a p-value of 0.079. What does this mean in the context of the test? We are 7.9% confident that the results of our test are correct.If the women of two countries have the same rates of coloring their hair, the probability of getting a difference at least this large is 0.079. If we take another sample, the probability of getting the same p̂China and…