A survey of contraceptive methods conducted by the National Center for Health Statistics in 1965 indicated that among 30-39 year old, married, nonpregnant women who practiced contraception 20% used some form of permanent contraception. The frequency of use of permanent contraception is suspected to have changed over the next 4 decades. To test this hypothesis, records were selected of 50 women subscribing to prepaid health plans in 2005 who were 30-39 year old, married, nonpregnant and practiced contraception. From these records 16 used some form of permanent contraception. Suppose we wish to test the hypothesis that a change has occurred in the true proportion of women who use permanent contraception without specifying the direction of that change. Suppose researchers are willing to commit the error of mistakenly rejecting the null hypothesis only 1% of the time. What is the significance level in this problem? Specify the null and alternative hypothesis Carry out the steps of the hypothesis test (calculate test statistic, p-value, and make a decision). If the true proportion of permanent contraception in 2005 was really 0.32, what is the power of this test with a sample size of 50.

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…

1. The percentage of 12- to 17-year-olds who reported talking at least once in the past year with their parents about the dangers of drug, tobacco, or alcohol is 60% nationally. A state youth council believes this proportion is higher in their state, where there has been an intense media campaign about this issue. A survey of randomly chosen students from across the state shows 1032 of 1642 students reporting they are having these conversations with their parents. Is there evidence that the percent of students using drugs, tobacco or alcohol in this state is above the national rate?

The National Academy of Science reported that 33 % 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 33 %. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 33 % ? 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. Answer Ho :p = 0.33 Ha P O # ο ο ο HAV O < 0.33 Tables Keypad Keyboard Shortcuts

A researcher takes a sample of 50 individuals and administers a background check to identify the number of prior arrests for each person. For whatever reason, one person is removed from the analysis and another random person is selected to replace that person. Having no additional information, what is your best guess of the number of prior arrests experienced by the replacement person? Why?

The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,476 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 153 of their customers and calculates that these customers used an average of 10,767 kWh of electricity last year. Assuming that the population standard deviation is 2478 kWh, is there sufficient evidence to support the power company's claim at the 0.05 level of significance? Step 3 of 3: Draw a conclusion and interpret the decision.

According to an​ almanac, 60​% of adult smokers started smoking before turning 18 years old. ​(a) If 300 adult smokers are randomly​ selected, how many would we expect to have started smoking before turning 18 years​ old? ​(b) Would it be unusual to observe 270 smokers who started smoking before turning 18 years old in a random sample of 300 adult​ smokers? Why?