Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with a = .01 for each of the following sample sizes. а. п 3 10 b. п 3D 20 с. п %3D 30
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- The corrosive effects of various soils on coated and uncoated steel pipe was tested by using a dependent sampling plan. The data collected are summarized below, where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the uncoated portion. Does this random sample provide sufficient reason to conclude that the coating is beneficial? Use ? = 0.01 and assume normality. n = 44, Σd = 224, Σd2 = 6268(a) Find t. (Give your answer correct to two decimal places.)(ii) Find the p-value. (Give your answer correct to four decimal places.)(b) State the appropriate conclusion. Reject the null hypothesis, there is significant evidence that the coating is beneficial.Reject the null hypothesis, there is not significant evidence that the coating is beneficial. Fail to reject the null hypothesis, there is significant evidence that the coating is beneficial.Fail to reject the null hypothesis, there is not significant evidence that the coating is beneficial.The corrosive effects of various soils on coated and uncoated steel pipe was tested by using a dependent sampling plan. The data collected are summarized below, where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the uncoated portion. Does this random sample provide sufficient reason to conclude that the coating is beneficial? Use a = 0.01 and assume normality. n- 40, Σd- 207, Σα? = 6199 (a) Find t. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer correct to four decimal places.) (b) State the appropriate conclusion. O Reject the null hypothesis, there is significant evidence that the coating is beneficial. Reject the null hypothesis, there is not significant evidence that the coating is beneficial. Fail to reject the null hypothesis, there is significant evidence that the coating is beneficial. Fail to reject the null hypothesis, there is not significant evidence that the coating is beneficial.Q. 23 Given the nine sample values 4.5, 6.5, 3.8, 4.2, 7.7, 8.5, 9.4, 5.3, 3.9 from a normal distribution with mean u and variance 4. Find the best critical region for testing Ho: µ = 4 vs. H,: µ = 5 of size 0.05. Also calculate the power of the test. %3D
- a sample of 60 grade 9 student age was obtained to estimate the mean age of all grade 9 students. x = 15.3 years and the population variance is 16Q. 23 Given the nine sample values 4.5, 6.5, 3.8, 4.2, 7.7, 8.5, 9.4, 5.3, 3.9 from a normal distribution with mean μ and variance 4. Find the best critical region for testing Ho: μ = 4 vs. H₁: μ = 5 of size 0.05. Also calculate the power of the test.suppose that for x=3, the predicted value is y=6. The data pair (3, 8) is part of the sample data. What is the value of the residual of x=3?
- Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x = 101.16, y = 102.3, r= 0.810, P-value = 0.000, and y = 23.09+0.78x, where x represents the IQ score of the wife. Find the best %3D %3D %3D predicted value of y given that the wife has an IQ of 109? Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. .... The best predicted value of y is . (Round to two decimal places as needed.) Critical values of the pearson correlation coefficient r NOTE: To test Ho: p = 0 against H,: p#0, reject Ho |if the absolute value of r is greater than the critical value in the table. a = 0.05 a = 0.01 4 0.950 0.990 0.878 0.959 0.811 0.917 0.754 0.875 0.707 0.834 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 19 0.456 0.575 20 0.444 0.561 25 0.396 0.505 30 0.361 0.463 35 0.335 0.430 40…Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x = 99.67, y = 100.6, r=0.890, P-value = 0.000, and %3D %3D y = - 5.27 + 1.06x, where x represents the IQ score of the husband. Find the best predicted value of y given that the husband has an IQ of 104? Use a significance level of 0.05. | Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y is. (Round to two decimal places as needed.)Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.
- the assumption that the t test for independent samples makes regarding the amount of variability in each of the two groups is called the?6. (20PTS) The ascorbic acid concentration of five different brands of orange juice was measured. Six replicate samples of each brand were analyzed. The following partial ANOVA table was obtained. Variation Source SS df MS F Between juices 8.45 Within juices 0.913 Total a. Fill in the missing entries in the table. b. State the null and alternative hypothesis. c. Is there a difference in the ascorbic acid content of the five juices at the 95% confidence level?The pH of rain, measured at a weather station in Michigan, was observed for 39 consecutive rain storms. The sample mean is 4.6982 and the sample variance is 0.39623. Test the research hypothesis that the mean pH is less than 5.00, with α = 0.01.