C1. A computer spam filter is 98% effective at sending spam emails to my junk folder, but will also incorrectly send 1% of legitimate emails to my junk folder. Suppose that 1 in 10 emails are spam. What proportion of emails in my junk folder are actually legitimate emails? Explain your solution fully - you may use any results from the lectures provided you state them clearly.
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- Plant X manufactures 70 percent of a certain company's bicycles, and Plant Y manufactures 30 percent. It has been found that 4 percent of the bicycles manufactured at Plant X and 5 percent of the bicycles manufactured at Plant Y are defective. What percent of the bicycles manufactured by the company are not defective? O 87.2% O 91.3% O 95.5% O 95.7%Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.A sample of 60 stocks traded on the NYSE that day showed that 24 went up.You are conducting a study to see if the proportion of stocks that went up is significantly more than 0.3. You use a significance level of α=0.001α=0.001.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value =Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.A sample of 80 stocks traded on the NYSE that day showed that 11 went up.You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3. You use a significance level of α=0.02α=0.02.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail…
- 6. Accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an impact on the rates of death and injury. In foggy, rainy, and sunny conditions, 1/4, 1/8, and 1/21 of the accidents result in death, respectively. Sunny conditions occur 60% of the time, while rainy and foggy conditions each occur 20% of the time. Given that an accident without deaths occurred, what is the conditional probability that it was foggy at the time?How would you conduct a sample of people in your community so that you could see which flavors are most popular? Give specific details of how you would collect your data, and state how many responses would be sufficient.not A 1995 study by the School of Public Health reported that 87% of male students who live in a fraterity house are binge drinkers. The figure for fraternity members who are residents of a fraternity house is 71 %, while the figure for men who do not belong to a fraternity is 44 % Suppose that 11% of U.S. male students live in a fraternity house, 15% belong to a fraterity but do not live in a fraterity house, and 74% do not belong to a fraterity a. What is the probability that a randomly selected malp student is a binge drinker? b. If a randomly selected male student is a binge drinker, what is the probability that he lives in a fraterity house? The probability that a randomly selected male student is a binge drinker is 0.5509 (Type an integer or a decimal rounded to two decimal places as needed) CETTE
- Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 51 stocks traded on the NYSE that day showed that 22 went up. You are conducting a study to see if the proportion of stocks that went up is significantly more than 0.3. You use a significance level of a =0.05. = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O…When looking at the data for graduate school admissions between men and women, it is shown that about 45% of men are admitted but only 38% of women. However, when the data is broken down by school it turns out that, within each school, the women are admitted at higher rates than the men. This could happen because I. The women apply in higher numbers to schools with lower acceptance rates. II. The women apply in higher numbers to schools with higher acceptance rates III. The men apply in higher numbers to schools with lower acceptance rates IV. The men apply in higher numbers to schools with higher acceptance ratesAn interdepartmental task force is being formed to investigate an increase in violent crimes. 1/5 of the task force will be police officers from the local precinct. 1/4 will be ATF agents, and the remaining 22 will be from the FBI. How many people are participating in the task force?
- A researcher is studying two types of medication that both treat hives. 23 out of the random sample of 270 adults given medication A still had hives 30 minutes after taking the medication. 15 out of another random sample of 300 adults given medication B still had hives 30 minutes after taking the medication. Test to see if the proportion of people who still had hives after medicine A is different than the proportion of people who still had hives after medicine B. Use a 0.01 level of significance. The correct hypotheses are: Ho:PA PB (claim) Ho :PA PB H A:PA < PB (claim) Но :РА На :РА # рв (claim) = PB Since the level of significance is 0.01 the critical value is 2.576 and -2.576 The test statistic is: 1.684 x (round to 3 places) The p-value is: 0.092 x (round to 3 places) The decision can be made to:A doctor wanted to study the effect of four different treatments on mental health. A group of 100 adults experiencing depression volunteered for the study. The doctor randomly assigned one-fourth of them to each of four groups. Group 1 followed a specific exercise plan, group 2 followed a specific diet plan, group 3 followed an exercise and diet plan, and group 4 did not follow any plan. After 4 weeks, the doctor contacted each participant and asked them if they felt any better. The results are displayed in the table. The doctor would like to know if these data provide convincing evidence that the distribution of responses differs across the treatment groups in the population of all patients like these. The random condition is met. The 10% condition is not needed because random sampling did not take place. This table of expected counts shows that all expected counts are at least 5. What is the value of the chi-square test statistic? χ‑2 = 5.03 χ‑2 = 6.26 χ‑2 = 25.33 χ‑2 = 39.22
