A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0.90. The population proportion of kernels that will pop for Brand S is 0.85. Two independent random samples were taken from the population. The following table shows the sample statistics. The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0.03. Is the consumer group’s claim correct?