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Refer to Exercise 9.5. Is
9.5 Suppose that Y1, Y2,..., Yn is a random sample from a
Find the efficiency of
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Chapter 9 Solutions
Mathematical Statistics with Applications
- In an experiment, the first sample with n1 = 10 has a standard deviation of s1 = 0.5. The second sample with n2 = 8 has a standard deviation s2 = 0.7.Determine the 98% confidence interval for (s_1/2)/(s_2/2) which is the ratio of the population variance. the random sample with sizes n1 = 16 and n2 = 25 respectively were taken from two normal populations. the vairance for both samples were s21 = 48 and S22 = 26 respectively. using an appropriate hypothesis, carry out a test to determine whether the variance from the first population is higher than the variance from the second population. use \alpha = 0.05arrow_forwardLet X1, X2, …, Xn be a random sample from the Normal distribution N() (a) Using method of moments to estimate the parameters and . (b) Are those estimators unbiased?arrow_forwardTo test H0: σ=2.2 versus H1: σ>2.2, a random sample of size n=24 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s=2.9, compute the test statistic. (b) If the researcher decides to test this hypothesis at the α=0.05 level of significance, use technology to determine the P-value. (c) Will the researcher reject the null hypothesis?arrow_forward
- To evaluate the effect of a treatment, one sample of n=8 is obtained from a population with population mean: u=40 and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M=35. 1. If the sample variance is s^2=32, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05? (show work please, and state both experimental and statistical hypotheses, and state your decision regarding the H0. (all 4 steps of hypothesis test) 2a. If the sample variance is s^2=72, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05? (please show your work and state your decision regarding the H0.) 2b. Calculate Effect size by using r^2 (percentage of variance explained) and state the meaning of effect size.arrow_forwardLet X1, ..., Xn be a sample from an Poisson population with parameter λ.(a) Find the maximum likelihood estimator for λ.(b) Is the estimator unbiased?(c) Is the estimator consistent?arrow_forwardSuppose that you are given two random variables x and y and you take measurements and obtain x1 = 2.3%, x2 = −7.6%, x3 = 0.1% andy1 =60, y2 =120, y3 =80. Findthelineofbestfity=α+βx. Calculate the correlation coefficient r and perform a left-tailed hypothesis test for r with significance level 10%. Based on this test, should we use this line to find the value of y when x = .5%arrow_forward
- An auto manufacturer claims that the variance of the gas mileage in a model of a hybrid vehicle is 0.16. A random sample of 30 vehicles has a variance of 0.26. At alpha = 0.05, is there enough evidence to reject the claim? Assume the population is normally distributed.arrow_forwardThe NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?arrow_forwardA sample of size 11 produced a variance of 18. Is this sufficient to reject the null hypothesis that σ2 = 6 when tested using a 0.05 level of significance?arrow_forward
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