A group of 250 patients was randomly split into two groups of 125 patients. The first group of 125 patients was given treatment A, and 72 of them improved their condition. The second group of 125 patients was given treatment B, and 60 of them improved their condition. Perform a hypothesis test to investigate whether there is evidence of a difference between the two treatments. What is the p-value of the test?
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- Dr. Mackintosh believes a new olfactory therapy would be more successful in promoting weight loss among obese patients. His patients are first weighed and then randomly assigned to olfactory therapy, dance therapy, or a control condition. At the end of the three weeks, the amount of weight lost is recorded. The results indicate no significant difference in the amount of weight lost between the three conditions. If true differences existed between the conditions, but they were not detected, what kind of error occurred?An environmentalist wishes to conduct a hypothesis test on the percentage of cars driven in the city that are hybrids. Is it sufficient for him to use a simple random sample of 173 cars if hybrids currently account for 8%of the car sales in the country and he claims that the percentage of hybrids in the city is higher than that?Acne is a common skin disease that affects most adolescents and can continue into adulthood. A study compared the effectiveness of three acne treatments and a placebo, all in gel form, applied twice daily for 12 weeks. The study's 517 teenage volunteers were randomly assigned to one of the four treatments. Success was assessed as clear or almost clear skin at the end of the 12 week period. The results of the study can be seen in the table below. Using the appropriate statistical test, determine if there is significant evidence that the four treatments perform differently. If so, how do they compare.
- A former residential complex was found to be a Superfund site polluted with several hazardous materials. Tamela is an investigative journalist who would like to show whether the proportion of the residents of the complex who eventually died from cancer is greater than the regional average of 14%. She randomly selects 54 residents who lived in the complex and finds that 12 of those residents eventually died from cancer. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test? Select the correct answer below: Although the proportion follows a binomial model with two independent outcomes and the data are selected at random, the number of successes and the number of failures are not both greater than or equal to 5. Although the proportion follows a binomial model with two independent outcomes and the number of successes and the number of failures are both greater than or equal to 5, the…Previously, 3% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of mothers who smoke 21 cigarettes or more is less than 3% today. She randomly selects 145 pregnant mothers and finds that 3 of them smoked 21 or more cigarettes during pregnancy. Test the researcher's statement at the a = 0.1 level of significance. What are the null and alternative hypotheses? Họ: P = 0.03 versus H4: p < 0.03 (Type integers or decimals. Do not round.) Because npo (1- Po) =|| 10, the normal model V be used to approximate the P-value. (Round to one decimal place as needed.)ester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the six months following the exercise program. Below are the results. Employee Before After 1 6 5 2 6 2 3 7 1 4 7 3 5 4 3 6 3 6 7 5 3 8 6 7 At the 0.05 significance level, can he conclude that the number of absences has declined? Estimate the p-value. State the decision rule for 0.05 significance level. (Round your answer to 3 decimal places.) Compute the test statistic. (Round your answer to 3 decimal places.)
- A researcher wants to examine the effect of daily mental exercises on cognitive performance of people in early stages of Alzheimer's disease. She enrolled to her study n = 16 patients diagnosed with the early stage of Alzheimer's disease and all participants conducted daily mental exercises for a month. At the end of the program all enrolled patients took the MMSE test (i.e., Mini-Mental State Examination). The results show that the sample mean on the MMSE test was M = 23.6 with the standard deviation, s = 7. It is known that the MMSE mean in the population of patients with early Alzheimer's disease is µ = 20. Do these data show a significant effect of daily mental exercises on cognitive performance in early stages of Alzheimer's disease?An advertising agency collected a random sample of 300 businesses targeted with an advertising campaign for a large commercial bank. The sample was used to investigate the efficacy of the advertising campaign. One of the variables measured was whether the business was considering becoming a client of the bank. Of the businesses sampled, 50 of the 300 businesses reported that they were considering becoming a client of the bank. A hypothesis test was conducted to determine if this provides evidence that less than 20% of all businesses were considering becoming a client of the bank. Calculate the test statistic to two decimal places (2dp). Test statistic =Does the test result Provide sufficient evidence that light alcohol consumption has a negative impact on the driving performance of a sleep deprived driver. Why or why not
- The Salk vaccine against polio was tested in 1954 in a carefully designed field experiment. Approximately, 400,000 children took part in this experiment. Using a randomization procedure, the children were randomly divided into 2 groups of equal size, a treatment group, and a control group. The vaccine was given only to the children in the treatment group; the control group children received placebo injections. The children did not know which of the two groups they had been placed into. The diagnosticians also lacked this information. 57 children in the treatment group went on to contract polio, while 142 children in the control group contracted the illness. How likely would such a difference in outcomes be when the assignment to the treatment or control group had absolutely no effect on the outcomes?Public relation companies conducted two surveys about deodorants. The first survey asked a random sample of 500 men about their use of a natural deodorant. A second survey asked the same questions to a random sample of 550 women. In these two studies, 68% of men and 44% of women stated they were dissatisfied with the effectiveness of natural deodorants. Use these results to answer the following questions about the proportion of men and women's satisfaction with natural deoderants. (Round to the nearest whole person as needed). For the men, the number of success within the sample is . For the U.S. teens, the number of failures within the sample is . For the women, the number of success within the sample is . for the Canadian teens, the number of failures within the sample is .The manufacturer of a new racecar engine claims that the proportion of engine failures due to overheating for this new engine, (p1), will be no higher than the proportion of engine failures due to overheating of the old engines, (p2). To test this statement, NASCAR took a random sample of 115 of the new racecar engines and 120 of the old engines. They found that 12 of the new racecar engines and 9 of the old engines failed due to overheating during the test. Does NASCAR have enough evidence to reject the manufacturer's claim about the new racecar engine? Use a significance level of α=0.1 for the test. Step 1 of 6 : State the null and alternative hypotheses for the test. Step 2 of 6 : Find the values of the two sample proportions, pˆ1p^1 and pˆ2p^2. Round your answers to three decimal places. Step 3 of 6 : Compute the weighted estimate of p, p‾p‾. Round your answer to three decimal places. Step 4 of 6 : Compute the value of the test…
