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Before you solve Problems 5–14, first classify the problem as one of the following:
Chi-square test of independence or homogeneity
Chi-square goodness of fit
Chi-square for testing or estimating σ2 or σ
F test for two variances
One-way ANOVA
Two-way ANOVA
Then, in each of the problems when a test is to be performed, do the following:
- (i) Give the value of the level of significance. State the null and alternate hypotheses.
- (ii) Find the sample test statistic.
- (iii) Find or estimate the P-value of the sample test statistic.
- (iv) Conclude the test.
- (v) Interpret the conclusion in the context of the application.
- (vi) In the case of one-way ANOVA, make a summary table.
Education: Exams Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.
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Chapter 10 Solutions
Bundle: Understandable Statistics: Concepts And Methods, 12th + Jmp Printed Access Card For Peck's Statistics + Webassign Printed Access Card For ... And Methods, 12th Edition, Single-term
- Let Y be a continuous RV with PDF otherwise Find the CDF, Fry), of Y . Find an expression for pth, p € (0, 1), quantile of the distribution. Find E(Y) and V(Y). Find E(-2Y + 1) and V(-3Y - 2). Find E(Y3).arrow_forwardLet X be a continuous RV with CDF Find P(X < 0), P(-1 < X < 1) and P(0.5 < X). Based on your answers to the above questions, what is the median of the distribu-tion? Why Find the PDF, fx (x), of X.arrow_forwardA survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward
- Let X be a continuous RV with PDF where a > 0 and 0 > 0 are parameters. verify that f-∞ /x (x)dx = 1. Find the CDF, Fx (7), of X.arrow_forward6. [20] Let X be a continuous RV with PDF 2(1), 1≤x≤2 fx(x) = 0, otherwisearrow_forwardA survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward
- A survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03…arrow_forwardIn some applications the distribution of a discrete RV, X resembles the Poisson distribution except that 0 is not a possible value of X. Consider such a RV with PMF where 1 > 0 is a parameter, and c is a constant. (a) Find the expression of c in terms of 1. (b) Find E(X). (Hint: You can use the fact that, if Y ~ Poisson(1), the E(Y) = 1.)arrow_forward
- Suppose that X ~Bin(n,p). Show that E[(1 - p)] = (1-p²)".arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
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