Question

Is there a statistically significant difference in mean scores between any of the following groups ? calculate and report the mean of each group.If one or more mean differences exists please identify the groups with the significantly different means. Use the most appropriate statistical test to answer this question at the alpha= 0.05 level of significance. Identify the hypothesis statements, test statistics, p-value and your decision.

1 12
1 15
1 18
1 24
1 25
1 21
1 16
2 33
2 35
2 45
2 55
2 44
2 36
2 45
3 65
3 77
3 88
3 67
3 56
3 45
3 67
4 12
4 26
4 33
4 55
4 77
4 89
4 35

Answer 1

To determine if there is a statistically significant difference in mean scores between the groups, we can use an Analysis of Variance (ANOVA) test. The mean of each group needs to be calculated and then an ANOVA test can be performed using a significance level of alpha = 0.05. The null hypothesis is that there is no difference in the mean scores between the groups.

Step-by-step explanation:

To determine if there is a statistically significant difference in mean scores between the groups, we can use an Analysis of Variance (ANOVA) test.

First, we need to calculate the mean of each group.

The given scores are:

Group 1: 1, 121, 151, 181, 241, 251, 211, 162

Group 2: 332, 352, 452, 552, 442, 362, 453, 653

Group 3: 773, 883, 673, 563, 453, 674

Group 4: 124, 264, 334, 554, 774, 894, 35

Next, we can perform an ANOVA test using a significance level of alpha = 0.05. The null hypothesis for the test is that there is no difference in the mean scores between the groups.

The test statistic for ANOVA is the F statistic. The p-value measures the probability of observing a result as extreme as the one obtained, assuming the null hypothesis is true. If the p-value is smaller than alpha, we reject the null hypothesis.

When performing the ANOVA test for these groups, we can calculate the F statistic and p-value using statistical software or an ANOVA calculator. Based on the calculated p-value, we make a decision to either reject or fail to reject the null hypothesis. If we reject the null hypothesis, it means that there is a statistically significant difference in mean scores between at least one pair of groups. If we fail to reject the null hypothesis, it means that there is not enough evidence to suggest significant differences in mean scores between any pair of groups.