1. Assuming that the populations are normal, is there any evidence to suggest that the average home-run distances in at least two of the ballparks are different? Use α = 0.05. Perform the complete four-step summary. Be sure to list all of the values that you have previously calculated for the required four-steps including the two degrees of freedom.
2. Construct the Tukey 95% confidence intervals to isolate the pairs of means contributing to the overall difference. For each pair indicate whether the two means are different or not. Hint: Work on submitting three trials for the Tukey parameter and the standard error first. If you do not get them in three trials, continue submitting up to three trials for each of the confidence intervals until you get one correct. Then go back and submit the fourth trial for the previous parts. Do not submit the one trial for the significance until the interval is correct.
a)Calculate the Tukey parameter. Note that this is not the same as the critical value.
b)Calculate the standard error. Please use three decimal places.
1)
1 | 2 | 3 | 4 | |||
count, ni = | 34 | 34 | 34 | 34 | ||
mean , x̅ i = | 396.200 | 413.28 | 397.80 | 400.10 | ||
std. dev., si = | 15.880 | 21.600 | 20.850 | 26.330 | ||
sample variances, si^2 = | 252.174 | 466.560 | 434.723 | 693.269 | ||
total sum | 13470.8 | 14051.52 | 13525.2 | 13603.4 | 54650.92 | (grand sum) |
grand mean , x̅̅ = | Σni*x̅i/Σni = | 401.85 | ||||
square of deviation of sample mean from grand mean,( x̅ - x̅̅)² | 31.866 | 130.759 | 16.362 | 3.045 | ||
TOTAL | ||||||
SS(between)= SSB = Σn( x̅ - x̅̅)² = | 1083.445 | 4445.814 | 556.309 | 103.531 | 6189.098 | |
SS(within ) = SSW = Σ(n-1)s² = | 8321.755 | 15396.480 | 14345.843 | 22877.874 | 60941.951 |
no. of treatment , k = 4
df between = k-1 = 3
N = Σn = 136
df within = N-k = 132
mean square between groups , MSB = SSB/k-1 =
2063.0327
mean square within groups , MSW = SSW/N-k =
461.6815
F-stat = MSB/MSW = 4.4685
SS | df | MS | F | p-value | F-critical | |
Between: | 6189.098 | 3 | 2063.033 | 4.47 | 0.0051 | 2.67 |
Within: | 60941.951 | 132 | 461.681 | |||
Total: | 67131.050 | 135 | ||||
α = | 0.05 |
Ho: µ1=µ2=µ3=µ4
H1: at least two of the ballparks are different
df1 = 3
df2=132
F stat = 4.47
p-value<α , reject null hypothesis
conclusion: there is enough evidence that at least two of the
ballparks are different at α=0.05
1. Assuming that the populations are normal, is there any evidence to suggest that the average home-run distances in at...
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