n a large clinical​ trial, 394,634 children were randomly assigned to two groups. The treatment group consisted of 199,216 children given a vaccine for a certain​ disease, and 31 of those children developed the disease. The other 195,418 children were given a​ placebo, and 95 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of n1​, p1​, q1​, n2​, p2​,

As products come off a large assembly line, they are inspected for quality. They are placed into one of three categories: pass, fail, or need additional inspection. The manager claims that 80% of the products pass the inspection, 5% fail, and 15% need additional inspection. In an effort to increase the passing rate, the machines are recalibrated. After this recalibration, a random sample of 100 products is selected. It is discovered that 85 passed inspection, 2 failed, and 13 needed additional inspection. The manager would like to know if there is convincing evidence that the distribution has changed. What is the value of the chi-square test statistic and P-value? Find the chi-square table here. χ2 = 2.38, P-value is less than 0.0005 χ2 = 2.38, P-value is greater than 0.25 χ2 = 5.10, P-value is less than 0.0005 χ2 = 5.10, P-value is greater than 0.25

High levels of cholesterol in the blood are associated with higher risk of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart Study recruited middle-aged men with high cholesterol but no history of other serious medical problems to investigate this question. The volunteer subjects were assigned at random to one of two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took a placebo. During the next five years, 56 men in the gemfibrozil group and 84 men in the placebo group had heart attacks. Is the apparent benefit of gemfibrozil statistically significant?  Using the p-value that you get from your previous z-test statistic, would you conclude that gemfibrozil is probably effective?

A study was conducted at the local skate park to determine how caffeine affected the performance of skateboarders during competitions. 100 skateboarders were selected from an upcoming competition roster. The researchers chose a random entry then proceeded to select every 4th entry until the desired sample size was reached.On the day of the competition, the sample was split (at random) into two groups. Each member of Group "A" was given a cup of decaf coffee while each member of Group "B" was given a cup of coffee containing 100mg of caffeine. (The skateboarders did not know which type of coffee they received.) As the competition progressed, the scores for each skateboarder were tracked.

High levels of cholesterol in the blood are associated with higher risks of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart Study recruited middle-aged men with high cholesterol but no history of other serious medical problems to investigate this question. The volunteer subjects were assigned at random to one of the two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took a placebo. During the next five years, 56 men in the gemfibrozil group and 84 in the placebo group had heart attacks. Is the difference statistically significant at the alpha = 0.01 level?

High levels of cholesterol in the blood are associated with higher risk of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart Study recruited middle-aged men with high cholesterol but no history of other serious medical problems to investigate this question. The volunteer subjects were assigned at random to one of two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took a placebo. During the next five years, 56 men in the gemfibrozil group and 84 men in the placebo group had heart attacks. Is the apparent benefit of gemfibrozil statistically significant?    What is the value of the combined proportion (c)?  Round to four decimal places

In a large clinical​ trial, 394,108 children were randomly assigned to two groups. The treatment group consisted of 198,537 children given a vaccine for a certain​ disease, and 30 of those children developed the disease. The other 195,571 children were given a​ placebo, and 105 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts​ (a) through​ (d) below.

In a large clinical​ trial, 401,049 children were randomly assigned to two groups. The treatment group consisted of 200,607 children given a vaccine for a certain​ disease, and 33 of those children developed the disease. The other 200,442 children were given a​ placebo, and 121 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of: n1​, p1​, q1​, n2​, p2​, q2​, p​, and q.

A car dealer is interested in comparing the average gas mileages of four different car models. The dealer believes that the average gas mileage of a particular car will vary depending on the person who is driving the car due to different driving styles. Because of this, he decides to use a randomized block design. He randomly selects five drivers and asks them to drive each of the cars. He then determines the average gas mileage for each car and each driver. Can the dealer conclude that there is a significant difference in average gas mileages of the four car models? The results of the study are as follows.  Average Gas Mileage Driver Car A Car B Car C Car D Driver 1 3232 2222 3030 3939 Driver 2 2121 3939 3838 3737 Driver 3 2626 3131 3232 3939 Driver 4 3838 4040 2323 3434 Driver 5 3131 2929 2121 2222 Copy Data ANOVA Source of Variation SSSS dfdf MSMS Rows 174.2000174.2000 44 43.550043.5500 Columns 91.600091.6000 33 30.533330.5333 Error 607.4000607.4000 1212…

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?