Suppose an experiment is done with criminals released from prison in a certain state where the recidivism rate is 32%; that is, 32% of criminals return to prison within three years. One hundred random prisoners are made to attend a "boot camp" for two weeks before their release, and it is hoped that "boot camp" will have a good effect. Suppose 27 of those prisoners retum to prison within three years. The null hypothesis is that those attending boot camp have a recidivism rate of 32%, p = 0.32. Complete parts (a) through (c) below. a. What is p, the sample proportion of successes? (It is somewhat odd to call returning to prison a success.) p= (Type an integer or a decimal. Do not round.) b. What is Po, the hypothetical proportion of success under the null hypothesis? Po =0.32| (Type an integer or a decimal. Do not round.)

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…

In a previous poll, 38% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 1186 adults with children under the age of 18 were selected at random, and 428 of those 1186 adults reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the α = 0.01 significance level. Because npo (1-Po) = 279.4 > 10 and the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? но: р = 0.38 versus H₁: p (Type integers or decimals. Do not round.) Find the test statistic, Zo. < 0.38 Zo -1.36 (Round to two decimal places as needed.) = Find the P-value. P-value = (Round to three decimal places as needed.) less than 5% of the population size, and the adults in the sample were selected at random, all of…

A researcher is creating a new treatment protocol for Myelodysplastic Syndrome (MDS), a form of preleukemia.  Following the old treatment protocol, 28% of patients with MDS will develop leukemia within 5 years of MDS diagnosis.  He believes his new treatment protocol will lead to fewer MDS patients developing leukemia.  He takes a random sample of 100 individuals on his new treatment protocol.  Of these 100 individuals, 20 develop leukemia within 5 years of MDS diagnosis.   In questions 8-9, create a 98% confidence interval for the true proportion of all MDS patients on this new treatment who will develop leukemia within 5 years of MDS diagnosis. What is the confidence interval? Do not round your answer. What is the interpretation of your confidence interval?

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…

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…

A news article estimated that only 6% of those ages 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans ages 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.06. (a) A random sample of  n = 100  people will be selected from this population and p̂, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.) meanstandard deviation (b) Is the sampling distribution of p̂ approximately normal for random samples of size  n = 100?  Explain. (Select all that apply.) the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is…

A local school board believes there is a difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school- aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Let p3= the true proportion of households with school-aged children that would support starting the school year a week early and pw= the true proportion of households without school-aged children that would support starting the school year a week earlier. The P-value for this significance test is 0.000034. Which of the following is the correct conclusion for this test of the hypotheses Ho: P;- Pw=0 and H, P,- Pw0 at the a =…

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? (Select the correct symbols and use decimal values not percentages.) 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…