Question

62, two independent samples of n1 = 8 and n2 = 10 were taken. The data is given below. Both populations are (1 point) In a test of two population means - M1 versus u2 - with unknown variances o normally distributed. Sample From Population 1: 15, 19, 20, 20, 22, 18, 17, 14 Sample From Population 2:11, 14, 15, 23, 25, 12, 20, 14, 22, 17 (a) You wish to test the hypothesis that both populations have the same variance. Choose the correct statistical hypotheses. A. HO :07 = ož HA:07 > oz OB. Ho: S} = SŽ HA:S} # SZ OC. Ho : 01 = ož HA: 0} <ož OD. Ho : 07 ož HA:07 = ož OE. Ho : oſ = ož HA:07 7 ož (b) Determine the value of the test statistic for this test. Use two decimals in your answer. Levene's Test Statistic = (c) Determine the P-value for this test, to three decimal places. P= (d) Using a = 0.05, the null hypothesis should ? From this data, the variation in Population 1 is ? the variation in Population 2.

Answer 1

a)

OE. I : 7 - Hu:07 #ਬ

b)

Sample 1 Sample 2 Skewness -0.292555 0.333171 Normality 0.9253 0.4776 Outliers Mean 18.12500 17.30000 S 2.695896 4.900113

Source Sum of Square Mean Square F Statistic P-value Groups (between groups) 17.34 17.34 3.43 0.082 Error (within groups) 16 80.77 5.05 Total 98.11 5.77

c)

1. Ho hypothesis Since p-value > a, Ho is accepted. The averages of all groups considered to be equal. In other words, the difference between the variances of all the groups, is not big enough to be statistically significant. 2. P-value p-value equals 0.0824035, [p(x = F) = 0.917597 ]. This means that if we would reject Ho, the chance of type 1 error (rejecting a correct Ho) would be too high: 0.08240 (8.24%) The bigger the p-value the stronger it support Ho 3. The statistics The test statistic F equals 3.433956, is in the 95% critical value accepted range: [-00:4.4940] 4. Effect size The observed effect size f is large (0.46). That indicates that the magnitude of the difference between the averages is large. The nequals 0.18. It means that the group explains 17.7% of the variance from the average (similar to R2 in the linear regression) 5. Tukey HSD / Tukey Kramer There is no significant different between the variances of any pair.

d) Do not reject the null hypothesis, Variation in population 1 = Variation in population 2