**Description of the Image:**The image contains text related to comparing two teaching methods for third grade students and their effects on reading test scores. It presents a statistical scenario, involving a sample of students taught with an old curriculum and another with a new curriculum. Here's a detailed breakdown:---**Introduction to the Scenario:**A group of third grade students is taught using a new curriculum, while a control group is taught using the old curriculum. The reading test scores for both groups are displayed using a back-to-back stem-and-leaf plot. The question is whether the new teaching method produces higher reading test scores than the old method, with the significance level set at \(\alpha = 0.10\).**Data Representation:**- **Old Curriculum (left side of the stem-and-leaf plot):** - 9 | 3 - 8 | 9 7 6 5 5 3 1 0 - 7 | 6 5 4 1 0 - 6 | 7 5 4 - 5 | 7 4 4 1 0- **New Curriculum (right side of the stem-and-leaf plot):** - 9 | 9 9 0 - 8 | 8 9 - 7 | 0 1 2 2 3 3 7 7 8 8 9 9 - 6 | 0 1 3 5 6 7 9 9 - 5 | 8 3 9- **Key:** 4|7|0 = 74 Old and 70 New**Statistical Analysis Steps:**(a) **Identify the Claim:**Choose the correct claim from the following options:- A. The new method produces higher reading test scores than the old method.- B. The new method produces equal reading test scores to the old method.- C. The new method produces lower reading test scores than the old method.- D. The new method produces different reading test scores than the old method.**Hypothesis Setup:**- Null Hypothesis (\(H_0\)): \(\mu_1 = \mu_2\)- Alternative Hypothesis (\(H_a\)) is selected using a dropdown, but visually shown as \(<

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Uploaded: 2024-03-20T07:06:27.000Z
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Description: **Description of the Image:**The image contains text related to comparing two teaching methods for third grade students and their effects on reading test scores. It presents a statistical scenario, involving a sample of students taught with an old c

Given: data list from the stem plot Old x1 New x2 39 40 47 58 49 59 50 60 51 61 53 62 55 62 56 63 56 63 57 67 59 67 60 68 61 68 61 69 64 69 65 70 67 71 67 73 68 75 76 77 79 79 83 89(a) Option (A) is correct The new method of teaching reading produces higher reading test scores than the old scores. (b) Nulll hypothesisH0: μ1≥μ2Alternative HypothesisH1: μ1<μ2 The claim is the Alternative Hypothesis which is μ1<μ2 (C) Calculation: Old x1 New x2 39 40 47 58 49 59 50 60 51 61 53 62 55 62 56 63 56 63 57 67 59 67 60 68 61 68 61 69 64 69 65 70 67 71 67 73 68 75 76 77 79 79 83 89 Sum 1085 1708 Mean 57.1053 68.3200 Standard Deviation 7.7237 9.8772 x1=57.1053 x2=68.3200s1=7.7237s2=9.8772 Degree of freedom =n1+n2-2=19+25-2=42 and the level of significance is =0.10 This is left tailed-test therefore Critical value is tdf,α=t42,0.10=-1.3025 Pooled standard deviation is sp=n1-1s12+n2-1s22n1+n2-2sp=19-17.72372+25-19.8772219+25-2=9.0174667 t-statistics t=x1-x2sp1n1+1n2=57.1053-68.32009.0174667119+125=-4.0862 Therefore t<-1.3025, reject the null hypothesis At the 10% significance level, there is enough evidence to support the claim.