1.2. Question 1 (q.2.1, page 75) - Theory Consider the following table based on a data set that has the sample size of 5 observations. - Ꮖ Image y Image 2 Image xy Image x- T Image (x)2 Image y - ỹ Image (x − ˜) (y — ÿ) ► Image - - 0 6 0 -2 (-2)² = 4 3.6 3.62-7.2 1 2 1 2 -1 (−1)² = 1 -0.4 -1 -0.4 0.4 2 3 4 6 0 0² = 0 0.6 3 1 9 3 1 (1)² = 1 -1.4 4 0 16 0 2 (2)² = 4 -2.4 0.0.60 1.-1.4-1.4 22.44.8 Στι ΣYi Σα ΣYixi Σ(xi) Image Σ(α; - π)2 Σ(y: - 3) - Σ(xi — x) (Yi — ÿ) 10 12 30 11 10 0 -13 (a) Using the values above, calculate the estimates for the intercept 61 and slope 62. (b) Using the numerical values above, show that Σ(x − x)² = - x² – Nò and Σ(xi - x) (yi – y) = Σ x iyi - Nx + y XiYi

8.4.1B. In a​ 4-week study about the effectiveness of using magnetic insoles to treat plantar heel​ pain, 51 subjects wore magnetic insoles and 43 subjects wore nonmagnetic insoles. The results are shown at the right. At α=0.06​, can you support the claim that there is a difference in the proportion of subjects who feel better between the two​ groups? Assume the random samples are independent. Complete parts​ (a) through​ (e).   Do you Feel​ Better? A circle graph titled Magnetic Insoles is divided into two sectors with labels and approximate sizes as a percentage of a circle as follows: Yes, 15, 29.41 percent; No, 36, 70.59 percent. Magnetic Insoles Yes 15No 36 A circle graph titled Nonmagnetic Insoles is divided into two sectors with labels and approximate sizes as a percentage of a circle as follows: Yes, 21, 48.84 percent; No, 22, 51.16 percent. Nonmagnetic Insoles Yes 21No 22 ​(b) Find the critical​ value(s) and identify the rejection​ region(s).   The…

6. Gravetter/Wallnau/Forzano, Essentials - Chapter 8 - End-of-chapter question 9 The psychology department is gradually changing its curriculum by increasing the number of online course offerings. To evaluate the effectiveness of this change, a random sample of n = 36 students who registered for Introductory Psychology is placed in the online version of the course. At the end of the semester, all students take the same final exam. The average score for the sample is M = 76. For the general population of students taking the traditional lecture class, the final exam scores form a normal distribution with a mean of μ = 71. If the final exam scores for the population have a standard deviation of σ = 12, does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Use a two-tailed test with α = .05. z-critical = ±    z =     These results indicate: Failure to reject the null hypothesis; the…

Let X ,X , ,X 1 2 n … be a random sample of size nfrom a population with mean μ and variance σ2.(a) Show that X2 is a biased estimator for μ2.(b) Find the amount of bias in this estimator.(c) What happens to the bias as the sample size n increases?

Suppose a linear model y=β0+β1xy=β0+β1x is fit to a sample data set, and a test of the null hypothesis H0:β1=0H0:β1=0 against an alternative hypothesis HA:β1≠0HA:β1≠0 is performed; a PP-value of 0.4203 is obtained. Which of the following scatter plots depicts the data set on which this model was fit and the hypothesis test was performed?

Section 10.2 Question #4 Suppose IQ scores were obtained for 20randomly selected sets of siblings. The 20 pairs of measurements yield x=101.34​, y=100.35​, r=0.856​, ​P-value=​0.000, and y=3.75+0.95x​, where x represents the IQ score of the older child. Find the best predicted value of y given that the older child has an IQ of 108​? Use a significance level of 0.05.   View the critical values of the Pearson correlation coefficient r. Critical values of the pearson correlation coefficient r n α=0.05 α=0.01 ​NOTE: To test H0​: ρ=0 against H1​: ρ≠​0,reject H0 if the absolute value of r is greater than the critical value in the table. 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 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…

A random sample of n1 = 14 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 19. For Englewood (a suburb of Denver), a random sample of n2 = 12 winter days gave a sample mean pollution index of x2 = 37. Previous studies show that σ2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. (a) State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 < μ2; H1: μ1 = μ2     H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.     The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We…

A sample is selected from a population with μ = 50 and σ = 12. If the sample mean of M = 56 produces a z-score of z = +1.00, then how many scores are in the sample?

Consider a multinomial experiment with n = 360 and k = 3. The null hypothesis is H0: p1 = 0.60, p2 = 0.25, and p3 = 0.15. The observed frequencies resulting from the experiment are: (You may find it useful to reference the appropriate table: chi-square table or F table) Category 1 2 3 Frequency 220 82 58   a. Choose the appropriate alternative hypothesis. All population proportions differ from their hypothesized values. At least one of the population proportions differs from its hypothesized value.   b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) b-2. Find the p-value. p-value  0.10 0.05  p-value < 0.10 0.025  p-value < 0.05 0.01  p-value < 0.025 p-value < 0.01   c. At the 10% significance level, what is the conclusion to the hypothesis test? Do not reject H0 since the p-value is more than significance level. Reject H0 since…

If all other values are held constant, what happens to the value of t when sample size increases ?