Problem 2: Styles of Instruction A researcher wanted to know whether there was a

Question

Problem 2: Styles of Instruction A researcher wanted to know whether there was a difference in the level of understanding among students learning StatCrunch based on the style of instruction. In a previous semester of STAT 250, Section 1 was taught StatCrunch with video tutorials and Section 2 was taught StatCrunch with written instructions. A random sample of 24 was taken from each section and the students in each sample were given a StatCrunch quiz that tested basic procedures. The data provided in StatCrunch represent the quiz scores the students received. The file is called "Styles of Instruction." At the 0.01 significance level, can the researcher conclude from these data that there is a significant difference in quiz scores between the two methods of instruction? a) Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. i. ii. State the null and alternative hypotheses using correct notation. State the significance level for this problem. ii. Calculate the test statistic "by-hand." Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. iv. Calculate the p-value using StatCrunch. v. State whether you reject or do not reject the null hypothesis and your reason for your answer in one sentence. vi. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences. vii. Use StatCrunch (Stat T Stats ) to verify your test statistic and p-value. Copy and paste this box into your document. b) Construct a 99% confidence interval using the above data. Please do this "by hand" using the formula and showing your work (please type your work, no images accepted here). Then, verify your result using StatCrunch. Copy and paste your StatCrunch result in your document as well. Interpret the confidence interval as we learned in class.

Explanation / Answer

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 # 0 i.e. (1 2)

            

Assuming population variances are equal, we would have to calculate pooled-variance t-Test

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (24-1)*3.01^2+(24-1)*6.51^2/23+23

         = 25.702

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(86.04-81.78)-0/25.702(1/24+1/24)

       =4.26/1.4635

       =2.91

The P-Value is 0.005553. The result is significant at p < .01 which means that reject the null hypothesis. Thus, we conclude that there is a difference between the quiz scores of two methods of instruction.

Section 1 Section 2 80.2 84.6 86.2 70.8 91.2 86.8 85.4 94.8 86.4 76.7 85.6 89.8 82.5 82.6 83.9 84.3 86.1 73.7 83.4 83.9 85.2 83.3 89.2 83.3 88.1 80.3 80.7 89.5 90.5 75.1 88.8 78.7 84.1 83.4 87.8 76 89.1 79.3 90 88.7 87.5 74.9 82.2 77.8 84.5 72 86.4 92.5 86.04166667 81.78333333 Average 3.005924103 6.509168562 SD

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