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- A study was performed on 200 elementary school students to investigate whether regular Vitamin A supplementation was effective in preventing colds during the month of March. 100 were randomized to receive daily Vitamin A supplements during the month of March, and 100 students were randomized to a placebo group (and did not receive Vitamin A) during the same month. The number of students getting at least one cold in March was computed in the two groups, and the results are given in the following 2 X 2 table. Using a 5% level of significance determine whether there is an association between Vitamin A supplementation and prevention of Common Cold ColdNo Cold Vitamin A1585100 Placebo2575100 40160200The manufacturer of a new racecar engine claims that the proportion of engine failures due to overheating for this new engine, (p1)(�1), will be no higher than the proportion of engine failures due to overheating of the old engines, (p2)(�2). To test this statement, NASCAR took a random sample of 235235 of the new racecar engines and 190190 of the old engines. They found that 2424 of the new racecar engines and 1111 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�=0.1 for the test.According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.33.Suppose a random sample of 109 traffic fatalities in a certain region results in 47that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the α=0.05 level of significance?
- A researcher conducts a study in which k = 6 and n= 6 per group. What are the critical values for the one-way betewwn-subjects ANOVA at a .05 sidnificance?A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self- improvement course would like to do so. The firm did a similar study 10 years ago and found that 70% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. The company tests to determine at the 0.01 level whether the population proportion has changed from the previous study. Which of the following is most correct? Reject the null hypothesis and conclude that there is sufficient evidence that the proportion of employees who are interested in a self-improvement course has changed over the past 10 years. Do not reject the null hypothesis and conclude that there is not sufficient evidence that the pro- portion of employees who are…According to a local chamber of commerce, in 1993, 5.9% of local area residents owned more than five cars. A local car dealer claims that the percentage has increased. He randomly selects 180 local area residents and finds that 12 of them own more than five cars. Test this car dealer's claim at the level of significance of 0.05.
- According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.36. Suppose a random sample of 110 traffic fatalities in a certain region results in 49 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the α=0.05 level of significance?A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of 90 urban residents showed that 12 subscribed, and a random sample of 97 suburban residents showed that 17 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 1% level of significanceHistorically, the proportions of all Caucasians in the United States with blood phenotypes A, B, AB, and O are .41, .10, .04, and .45, respectively. To determine whether current population proportions still match these historical values, a random sample of 200 American Caucasians were selected, and their blood phenotypes were recorded. The observed numbers with each phenotype are given in the following table.ABABO89181281Is there sufficient evidence, at the .05 level of significance, to claim that current proportions differ from the historic values?a) State the hypotheses.b) Find the critical value at the 5% significance level (rounded off to four decimals).c) Calculate the value of the Chi-square test (rounded off to two decimals).d) State the conclusion at the 5% significance level
- The manufacturer of a new racecar engine claims that the proportion of engine failures due to overheating for this new engine, (p1)(p1), will be no higher than the proportion of engine failures due to overheating of the old engines, (p2)(p2). To test this statement, NASCAR took a random sample of 215215 of the new racecar engines and 240240 of the old engines. They found that 2222 of the new racecar engines and 1010 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=0.1α=0.1 for the test. Step 4 of 6 : Compute the value of the test statistic. Round your answer to two decimal places.Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here. Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6 Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21 Part A: Do the data provide convincing evidence, at the α = 0.02 level, that the glucose drug is effective in producing a reduction in mean glucose level? Part B: Create and interpret a 98%…The supply management of a certain company suggested adopting the water-on-demand system in restaurants on a certain island, in order to conserve water. A restaurant owner stated that 30% of customers do not drink water, and therefore water conservation would be due not only to the water not drunk in each glass, but also to the water saved by washing the glasses. Suppose a sample of 480 restaurant patrons indicated that 128 do not drink water. Test the restaurant owner's claim at the 0.05 level of significance.