A researcher wanted to determine if teaching approaches influence second graders’ ability to do columnar addition. To test this, the researcher randomly selected 75 second graders from a local school and assigned them to one of three teaching conditions: (1) rote memory, (2) manipulatives, or (3) computer. One group of 25 students were taught using rote memory, a second group of 25 students was taught using manipulatives, and a third group of 25 students was taught with a calculator. All students were given a test on columnar addition. The means and standard deviations for the three groups are shown below.Mean Number of Correct Answers for Three Groups of Second Grade Students on a Test of Columnar AdditionGroup n M SDRote Memory 25 4.00 2.24Manipulatives 25 9.00 3.08Calculator 25 17.00 2.74What hypothesis testing technique should the researcher use to analyze the data? Two-sample t-test Paired t-test z-test for the population mean ANOVA

A statistics professor implemented an online homework system for their introductory statistics  courses and wanted to know whether the system improved test scores.  In the Fall semester, homework was completed with pencil and paper, checking answers in the back of the book. In the Spring semester, homework was completed online – giving students instant feedback on their work. The results are summarized below.  Assume that the sampled populations are normal with equal variances.  Fall Semester(pencil and paper)Spring Semester(online system)Number of Students1416Mean Test Score73.477.4Sample Standard Deviation10.211.1  Is there evidence to suggest that the online system improves test scores? Use α = 0.05. Here  μ1𝜇1 = true mean score under pencil and paper system, and  μ2𝜇2  = true mean score under online system.

Which teacher is most effectively using mnemonics?

Carl is conducting a study to determine the effects of the new technology-assisted learning methods among students. As part of this study, he has selected a group of university students, male and female, in the age group of 18 to 24 years. These students have been using the new methods of learning. In terms of research methodology, this group best describes a _____. a. population b. placebo group c. control group d. sample

Using four methods to teach ANOVA, do these four samples differ enough from each other to reject the null hypothesis that type of instruction has no effect on mean test performance?Method to teach ANOVA Mean SD Nmethod 1 (single teacher) 4.85 0.360 34method 2 (co-teachers) 4.61 0.715 31method 3 (computer) 4.61 0.688 36method 4 (lab) 4.38 0.793 32Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that test score is related to teaching method.One of the conditions that allows us to use ANOVA safely is that of equal (population) standard deviations. Can we assume that this condition is met in this case? Yes, since 0.793 − 0.360 < 2. No, since 0.793/0.360 > 2 No, since the four sample standard deviations are not all equal. No, since the population standard deviations are not given, so we cannot check this condition.

Using four methods to teach ANOVA, do these four samples differ enough from each other to reject the null hypothesis that type of instruction has no effect on mean test performance?Method to teach ANOVA Mean SD Nmethod 1 (single teacher) 4.85 0.360 34method 2 (co-teachers) 4.61 0.715 31method 3 (computer) 4.61 0.688 36method 4 (lab) 4.38 0.793 32Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that test score is related to teaching method.Let μ1, μ2, μ3, and μ4 be the mean test scores for teaching using methods 1, 2, 3, and 4 respectively. Which of the following are the appropriate hypotheses in this case?H0: µ1 = µ2 = µ3= µ4Ha: µ1, µ2, µ3, µ4 are not all equalH0: µ1 − µ2 < 0Ha: µ1 − µ2 = 0H0: µ1 = µ2 = µ3= µ4Ha: µ1 ≠ µ2 ≠ µ3≠ µ4H0: µ1 ≠ µ2 ≠ µ3 ≠ µ4Ha: µ1 = µ2 = µ3 = µ4