Question

To examine the potential effects on the transmission of dengue, Bian et al. (2010) infected mosquitoes from both the WB1 (laboratory created) strain and the original wild strain with dengue. Fourteen days later, the mosquitoes were allowed to feed on an artificial food solution for 90 minute. Viral titers in the food solution were then measured in plague feeding units per ml. The results are given below. Mosquitoes were tested in groups, and so each data value is an average for the group, measured in plaque feeding units per ml. The data have already been log-transformed using log(Y+1), to better visualize the differences.

WB1: n₁ = 9    R₁ = 40.5

Wild: n₂ = 12    R₂ = 3

H0: the distribution of viral titers is the same between the two strains

HA: the distribution of viral titers is not equal

The data has been ranked from smallest to largest andthe rank sum (R₁, R₂) for each data set are listed above. Carry out a Mann-Whitney U-test on the WB1 data and solve for U₁. Answer to one decimal place.

Answer 1

H0: The two populations are equal

H1: The two populations are not equal

Let the los be alpha = 5%

Test Statistic U = min(U₁, U₂)

Where, U₁ = n₁n₂ + ((n₁+(n₁+1))/2 -R₁ and U₂ = n₁n₂ + ((n₂+(n₂+1))/2 -R₂

Where R₁ and R₂ are the sums of the ranks in group 1 and 2 respectively.

U₁ = n₁n₂ + ((n₁+(n₁+1))/2 -R₁

=9*12+((9+10)/2-40.5

=77

U₂ = n₁n₂ + ((n₂+(n₂+1))/2 -R₂

₌9*12+((12+13)/2-3

=117.5

Test Statistic U = min(U₁, U₂) = min(77,117.5) = 77

Critical value of U = 26 from Mann Whitney U table

Here test statistic U 77 > Critical U 26 so we reject the null hypothesis.we conclude that the two populations are not equal.

Hope this will be helpful. Thanks and God Bless You :)