7. A study shows that 80% of the population was vaccinated against the Venusian flu but 2% of the vaccinated population got the flu anyway. If 10% of the total population got this flu, what percent of the population either got the vaccine or got the disease?
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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- Helena gathers data about the music preferences of users of a social media application. She gathers information on music events (MEs). In her study, a music event is defined as a posting that has a hashtag or is linked to other video- sharing websites. 1. From her data, Helena claims that about 15% of MEs on the application are hip hop/rap. Juan wants more proof of her claim. • Juan uses technology to determine the genres of music of 100 MEs he chooses at random. He determines that 9 were hip hop/rap. • Juan points out the 9% rate to Helena. Part A Assume Helena is correct and 15% of MEs on the app are hip hop/rap. Use random numbers and a simulated sampling distribution to simulate the outcome of several trials, in which each trial samples 100 MEs from the app and counts the number of hip hop/rap MEs. Make a histogram for your data. Is the model consistent with what you would expect? Explain.A researcher is studying two types of medication that both treat hives. 18 out of the random sample of 201 adults given medication A still had hives 30 minutes after taking the medication. 22 out of another random sample of 212 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 less than the proportion of people who still had hives after medicine B. Use a 0.05 level of significance. The correct hypotheses are: O Ho: PA HA PA Ho: PA HA PA O Ho: PA HA PA = PB PB(claim) The p-value is: PB PB(claim) PB PB(claim) Since the level of significance is 0.05 the critical value is -1.645 (round to 3 places) The test statistic is: (round to 3 places)An antidepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 245 patients who use the new version is selected by the researcher, and 178 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c)…
- An antidepressant has historically been known to relieve depression for 65% of patients who use the drug. The drug's formula was changed recently to include smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 65%. A random sample of 240 patients who use the new version is selected by the researcher, and 149 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. Ho :0 H¡ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ OSO (c) Find the…The national Park service monitors streams in Rainier national park for pollution and fish spawning habits. Suppose it is known that 40% of the streams in the park are either considered "polluted" or "known for spawning stream", 15% of the streams are classified as "polluted" and 35% of the streams are "known for spawning streams" what proportion of streams are known to be both polluted and known for spawning streams.A researcher is studying two types of medication that both treat hives. 18 out of the random sample of 201 adults given medication A still had hives 30 minutes after taking the medication. 22 out of another random sample of 212 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 less than the proportion of people who still had hives after medicine B. Use a 0.05 level of significance. The correct hypotheses are: O Ho: PA HA PA Ho: PA HA PA O Ho: PA HA PA = PB PB(claim) The p-value is: PB PB(claim) PB PB(claim) Since the level of significance is 0.05 the critical value is -1.645 (round to 3 places) The test statistic is: (round to 3 places)
- In January 2007 consumer reports published a study of bacteria infected chicken sold in the US. They purchased 525 broiler chickens from various stores in 23 states and tested them for bacterial contamination. Lab tests indicated 83 percent of the chickens were contaminated with campylobacter. how would you justify a claim by the usda that's the number of chickens tested was not large enough since 9 billion chickens are sold each year?2. The drug Ritalin is designed to stimulate the central nervous system. In a random sample of 242 boys aged ten - twelve years old, it was found that 68 of the boys were taking Ritalin. It is known that the proportion of all boys aged 13 - 15 who take Ritalin is 22%. A researcher claims that the population proportions of boys who take Ritalin aged 10 – 12 is different than boys aged 13 - 15. Can you support this claim at the 5% significance level? a. Conduct a hypothesis test to test the claim at the 5% significance level. Be sure to state you Ho and Ha, your test statistic and p-value, whether or not you reject Ho and whether you support the claim. b. Write a complete sentence describing what a Type I error is in context. c. Write a complete sentence describing what a Type II error is in context.In 2016, the New York Times reported that the average American spent 50 minutes per day on Facebook, as compared to an average of 42 minutes per day reading, exercising, or actually socializing combined. You suspect that this gap has widened over the years, and collect a random sample of 100 people. For 50 of them (again, randomly chosen from your sample), you track their time spent on Facebook; you track the other 50 peoples’ total time spent reading/exercising/socializing. (a) Say the 2016 figures regarding Americans’ time allotments still hold true. If the population standard deviation for minutes using Facebook is 12.5 minutes, and the population standard deviation for minutes spent on reading, exercising, and socializing (referred to from here on as ”Other” activities) is 8 minutes, what are the expected value and the standard error of the difference between the average amount of time spent on Facebook and the average amount of time spent on Other activities computed from a sample…
- 3. People lose muscle mass as they age. Suppose a person lost 7% of their muscle mass between ages 50 and 60 (based on what they had at age 50) and 8% of their muscle mass from 60 to 70 (based on what they had at age 60). What percentage of the muscle mass that they had at age 50 have they lost by age 70? The following approach is INCORRECT! Explain why. The person lost 1% and then lost 8%. Since 1% + 8% =15%, they lost 15%. Explanation: Work: Answer the question, supporting your answer with work.An antidepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 215 patients who use the new version is selected by the researcher, and 159 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value…Two different blood pressure medicines are being compared to determine if the average reduction in blood pressure is the same for each medication. The goal of the study is to determine if the medications differ. Twenty men age 50-60 years old are selected for the study. Ten men are chosen at random to receive the first medication and the other 10 men receive the second medication. Each of the 20 men is monitored for one month to determine the change in blood pressure over that time. Minitab provides the 95% confidence interval for (mu1 - mu2) (2.63, 14.18) a. Interpret this 95% CI. b. What assumptions (be specific) are necessary to construct this CI?