Question

& 13.1.RA-2 Assigned Media Question Help By hand, determine the F-test statistic for the accompanying data by answering parts (a) through (below. BI! Click the icon to view the data. (a) Determine the mean of the entire set of data. X=8 (Type an integer or a decimal. Do not round.) (b) Find the sample mean for each sample. *3 - 10 (Type integers or decimals. Do not round.) (c) Find the sample variance for each sample. Practice Q: The ins 40 mp driver's similar (Type Integers or decimals. Do not round.) A See ans Q: A highwa Enter your answer in the edit fields and then click Check Answer The bar

Answer 1

Solution-

a) Mean of entire data is

Xbar = 8

b) Sample mean for each sample-

X1 bar = 6

X2 bar = 8

X3 bar = 10

c) sample variances are-

$S_1^2$ = 73.5

= 46.5

SE

$S_3^2$ = 14.5

●  F-test statistic

F = 0.446

◆ Test Calculation and results-

The total sample size is N =15 Therefore, the total degrees of freedom are: d ftotal = 15 – 1= 14 Also, the between-groups degrees of freedom are d fbetween=3–1 =2, and the within-groups degrees of freedom are: df within = = d ftotal – dfbetween 14 – 2 = 12 First, we need to compute the total sum of values and the grand mean. The following is obtained Xij = 30 + 40 + 50 = 120 Also, the sum of squared values is x ; = 474 + 506 + 558 = 1538 47 Based on the above calculations, the total sum of squares is computed as follows 2 Seous = – x3 - CE = = 1538 1202 15 578 i,j i,j

The within sum of squares is computed as shown in the calculation below: S Swithin SSwithingroups 294 + 186 + 58 = 538 The between sum of squares is computed directly as shown in the calculation below: The between sum of squares is computed directly as shown in the calculation below: Now that sum of squares are computed, we can proceed with computing the mean sum of squares: 40 M Sbetween SSbetween dfbetween 20 M Swithin = SSwithin df within 538 12 = 44.833 Now that sum of squares are computed, we can proceed with computing the mean sum of squares: 40 M Sbetween S Sbetween dfbetween 20 2 538 MSwithin S Swithin df within - 44.833 12 Finally, with having already calculated the mean sum of squares, the F-statistic is computed as follows: F = M Sbetween M Swithin 20 44.833 0.446

.(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: P1 = M2 = 43 Ha: Not all means are equal The above hypotheses will be tested using an F-ratio for a One-Way ANOVA. (2) Rejection Region Based on the information provided, the significance level is a =0.05and the degrees of freedom are dfi =2 and d f2 =2, therefore, the rejection region for this F-test is R ={F:F >Fc =3.885.} (3) Test Statistics F M Sbetween M Swithin = 20 44.833 = 0.446 (4) Decision about the null hypothesis Since it is observed that F =0.446 Fc =3.885it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p =0.6503and since p =0.6503 0.05it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that not all 3 population means are equal, at the a =0.05significance level.

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