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Finding Critical Values In constructing confidence intervals for σ or σ2, Table A-4 can be used to find the critical values
where k is the number of degrees of freedom and zα/2 critical z score described in Section 7-1. Use this approximation to find the critical values
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ESSENTIALS OF STATISTICS 6TH ED W/MYSTA
- Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by (1-e-x², x ≥ 0 ={1,- x<0 Find the probability that the random variable X falls within one standard deviation of its mean. Fx (x) =arrow_forwardA random sample of size n₁ = 14 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second random sample of size n₂ = 9 is taken from another normal population with mean 71 and standard deviation 11. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ – X₂ exceeds 4. 1 2 (b) The probability that 4.3 ≤ X₁ – X2 ≤ 5.6. Round your answers to two decimal places (e.g. 98.76). (a) i (b) iarrow_forwardNew employees at a company are required to attend a three-day training. For social distancing, the employees are split into two groups, one that attends in-person, and the other group attends via zoom. At the end of training, the same test is given to each group and the scores are given below. Can it be concluded that the in person group performed better on the training test? Use α=0.05. In person group: 56, 50, 52, 44, 52, 47, 47, 53, 45, 48, 42, 51, 42, 43, 44 Zoom group: 59, 54, 55, 65, 52, 57, 64, 53, 53, 56, 53, 57arrow_forward
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- A random sample of size n₁ = 16 is selected from a normal population with a mean of 75 and a standard deviation of 8. A second random sample of size n₂ = 9 is taken from another normal population with mean 70 and standard deviation 12. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ X₂, exceeds 4 (b) The probability that 3.5 ≤ X₁ – X₂ ≤ 5.5arrow_forwardThe χ2 critical value for n = 16 and a=0.01 for a left-tailed test is 5.812.arrow_forward2. If x is a value assumed by a random variable X having the exponential distribution given by x > 0, elsewhere f(x)= = 0 >0 Ө 0, Find k so that the interval 0 <0arrow_forwardA random sample of size n₁ = 14 is selected from a normal population with a mean of 75 and a standard deviation of 6. A second random sample of size n₂ = 7 is taken from another normal population with mean 68 and standard deviation 12. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ X₂ exceeds 4. (b) The probability that 4.7 ≤ X₁ - X₂ ≤ 5.9. Round your answers to two decimal places (e.g. 98.76). (a) i (b) iarrow_forwardIQ: Scores on a certain IQ test are known to have a mean of 100. A random sample of 51 students attend a series of coaching classes before taking the test. Let µ be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if µ>100. A test is made of the hypotheses Ho:H=100 versus H, :µ>100. Consider three possible conclusions: (i) The classes are successful. (ii) The classes are not successful. (ii The classes might not be successful. Part 1 of 2 Which of the three conclusions is best if H, is not rejected? The best conclusion is (Choose one) ▼ Part 2 of 2 Assume that the classes are not successful. Is it possible to make a Type II error? Explain. a type II error (Choose one) (Choose one) hypothesis is (Choose one) ▼ possible. The classes are not successful when the nullarrow_forwardWhich of the following is correct to determine the critical values for a chi-square test using the chi-square distribution table? I. If the test is right-tailed, then the critical value of χ2 corresponds to the probability value α. II. If the test is left-tailed, then the critical value of χ2 corresponds to the probability value 1−α. III. If the test is two-tailed, then the critical values of χ2 corresponds to the probability values a/2 to the right and 1−a/2 to the left.a. Ib. IIc. IIId. I, II, and IIIarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill