Please use minitab Refer to the oxygen partition study in reedfish conducted by

Question

Please use minitab

Refer to the oxygen partition study in reedfish conducted by Pettit and Beitinger The accompanying table gives the percentages of oxygen uptake by air (the rest is by water) for reedfish exposed to two temperature environments: one group of n_1 =11 reedfish in water at 25 degree C and the other group of n_2 = 12 reedfish in water at 33 degree C. Use the Minitab printout to answer the questions. a. Does the data in the table present sufficient evidence to indicate a difference between the percentages of oxygen uptake by air for reedfish exposed to water at 25 degree C and those at 33 degree C? Test using alpha = .05. b. What is die p-value for the test c. The Minitab analysis uses the pooled estimate of sigma^2. Is the assumption of equal variances reasonable? Why or why not? (not formal analysis) d. What assumption had to be made concerning the population variances so that the test would be valid? Do the data provide sufficient evidence to indicate that die variances viola

Explanation / Answer

a) (assumption equal population variance for two groups)

Two-sample T for 25c vs 33c

N Mean StDev SE Mean
25c 11 35.1 14.9 4.5
33c 12 47.1 11.6 3.4

Difference = mu (25c) - mu (33c)
Estimate for difference: -11.99
95% CI for difference: (-23.51, -0.47)
T-Test of difference = 0 (vs not =): T-Value = -2.17 P-Value = 0.042 DF = 21
Both use Pooled StDev = 13.2698

a) using the MINITAB output above test for difference of these two table

and we get p-value is 0.042<0.05 =significance level

hence we can reject H0, and claim that there is significant difference among the group.

c) pooled estimate is 13.26982= 176.087

d)

Test and CI for Two Variances: 25c, 33c

Method

Null hypothesis Sigma(25c) / Sigma(33c) = 1
Alternative hypothesis Sigma(25c) / Sigma(33c) not = 1
Significance level Alpha = 0.05

Statistics

Variable N StDev Variance
25c 11 14.876 221.291
33c 12 11.619 134.992

Ratio of standard deviations = 1.280
Ratio of variances = 1.639

95% Confidence Intervals

CI for
Distribution CI for StDev Variance
of Data Ratio Ratio
Normal (0.682, 2.451) (0.465, 6.008)
Continuous (0.663, 3.230) (0.440, 10.434)

Tests

Test
Method DF1 DF2 Statistic P-Value
F Test (normal) 10 11 1.64 0.429
Levene's Test (any continuous) 1 21 0.91 0.350

using this test we test for equality of two groups by two methos

based on these two method we get p-values are >0.05

hence we accept H0, and claim that our assumption in part a was vaild

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