Two different box-filling machines are used to fill cereal boxes on an assembly line, which affects the weight of the product in the boxes. It is known that the standard deviation of the weight of the product is o = 1.16 ounce, for both machines. Experiments are conducted using both machines with sample sizes of 35 each. Use the Central Limit Theorem to find the probability P(X1 – X₂ ≤ 0.29) under the condition µ₁ = µ2.
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- Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300, are selected, and 16 defective parts are found in the sample from machine 1, while 8 defective parts are found in the sample from machine 2. Is it reasonable to conclude that both machines produce the same proportion of defective parts? Use a = 0.05. (a) Test the hypothesis Ho: P₁ = P2 verses H₁: P₁ P2. What is zo? Round your answer to two decimal places (e.g. 98.76). Zo = (b) Is it reasonable to conclude that both machines produce the same proportion of defective parts?Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300, are selected, and 16 defective parts are found in the sample from machine 1, while 8 defective parts are found in the sample from machine 2. Is it reasonable to conclude that both machines produce the same proportion of defective parts? Use a = 0.05. (a) Test the hypothesis Ho: P1 = P2 verses H;: P1 # P2. What is zg? Round your answer to two decimal places (e.g. 98.76). Zo = (b) Is it reasonable to conclude that both machines produce the same proportion of defective parts? Statistical Tables and ChartsAn analogue signal received at a detector, measured in microvolts, is normally distributed with mean of 185 and variance of 244. What is the probability that is the signal will be less than 203 µV given that it is less than 184 µV?
- What is the kurtosis for the distribution of scores with a mean of 9.02 and a mode of 3?The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes n1 = 15 and n2 = 17 are selected, and the sample means and sample variances are x1 = 8.73, (s1)^2 = 0.35, x2 = 8.68, and (s2)^2 = 0.40. Assume that the population variances are equal and that the data are drawn from a normal distribution. Is there evidence to support the claim that the two machines produce rods with different mean diameters? Use a P-value in arriving at this conclusion.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 0.34. Suppose a random sample of 113 traffic fatalities in a certain region results in 52 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 x = 0.05 level of significance? Because npo (1-Po) = 25.4 > 10, the sample size is sample is given to be random, satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? Ho: versus H₁: (Type integers or decimals. Do not round.) less than 5% of the population size, and the the requirements for testing the hypothesis are