Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.6. Assume that the trials are independent a. Find the probability that the first successful alignment requires trials four trials at the maximum b. Calculate the mean of x c. Calculate the variance of x
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Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.6. Assume that the trials are independent
a. Find the probability that the first successful alignment requires trials four trials at the maximum
b. Calculate the mean of x
c. Calculate the variance of x
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- Consider a set of data (x₁, yi), i=1,2,..0 and the Simple linear regression equation given by : 4 y₁ = B₁+ B₁²x₁ The /s Standardized random variable of given by 2= B₂₁ - B²₁₂² FSSxx find the mean and the variance of ZoA study was conducted to examine the difference between the average cholesterol levels in the blood of men and females. It can be assumed that cholesterol levels follow a normal distribution in both populations and that the distribution in the populations is similar (e. Assume that cholesterol levels follow a normal distribution in both populations with similar variances). An equal number of measurements were made on men and women. The results were entered into R and the R code and output can be seen below: t.test(kol$mael-kol$kyn,var.equal = T) %3D Two Sample t-test data: kol$mael by kol$kyn t = 5.7731, df = 18, p-value alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 15.28775 32.78050 = 0.000018 sample estimates: mean in group Men mean in group women 219.2115 195.1774 1. Which statement is best based on the results of the study? Use a=0.05. a. The P-value is lower than a and therefore can be rejected HO b. The P-value is higher than a…The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Jelly Belly Candy Company is testing two machines that use different technologies to fill three pound bags of jelly beans. The following tables contain a sample of data on the weights of bags (in pounds) filled by each machine. Machine 1 Machine 2 Ho: 01 2 Ho: 01 State the null and alternative hypotheses. 2 2 Ha: 01 Ha: 01 2.95 3.45 3.50 3.75 3.48 3.26 3.33 2 Ha: 01 ≤0₂ 3.16 3.20 3.22 3.38 3.90 3.36 3.25 2 3.20 2 3.12 Ho: 01 Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion? = 2 Ho: 01 #0 2 02 = 2 2 02 02 2 2 2 ≤02 3.20 2 2 H₂: 01 > 02 3.28 3.22 2.98 3.45 3.70 3.34 3.18 3.35 3.22 3.30 3.34 3.28 3.29 3.25 3.30 3.27 3.38 3.34…
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- A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…Let Y be the life in hours of a battery. Assume Y is normally distributed with mean 200 and variance o?. If a purchaser of such batteries requires that at least 90% of the batteries have lives exceeding 150 hours, what is the largest value o can be and still have the purchaser satisfied?The data shown in the table represent the measurements of 10-kΩ resistors (in kΩ) produced from five different machines. A random sample of nine resistors from each machine is taken to determine whether the mean resistance varies from one machine to another. Perform analysis of variance and test the hypothesis at the 0.05 level of significance that the mean resistances differ significantly for the five machines, all through manual computations. Show all complete and systematic solutions.
