A researcher is concerned about the level of knowledge possessed by university s

Question

A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. The results are given in Table 1 below Education Business/Management Behavioral/Social Science Fine Arts 62 81 75 58 67 48 26 36 57 34 48 53 24 48 25 82 52 47 80 49 74 68 70 57 87 64 28 29 51 65 Using these data, the rescarcher performed an ANOVA test, which resulted in the following ANOVA table (Table 2). Unfortunately, a few of the cells in the table have been lost. MS P-value 0.0478 DF F crit Treatments 2538.59 Error Total 28 10464.72 a. (Worth 3 points) Complete the ANOVA table using the known values in the table. (Round SS & MS to 2 decimal places. Round F, p-value and F critical to 4 decimal places. b- (Worth 2 points) Based on this completed ANOVA table, can the researcher conclude that there is a significant difference between the four testing conditions? Use a 0.05 level of significance. Be sure to indicate hypotheses, dectstons, and conclustons

Explanation / Answer

a)

b)

Here the hypothesis are

H0: mu1 = mu2 = mu3 = mu4

H1: at least two means are different

As p-value is less than the significance level of 0.05, reject null hypothesis

Hence there are significant evidence to conclude that at least two means different

SS DF MS F P-value F crit Treatments 2538.59 3 846.20 2.9893 0.0478 2.9467 Error 7926.13 28 283.08 Total 10464.72

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