# A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop

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. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0.92 Brand S 200 0.89 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? Yes. The mean is 0.92−0.89=0.03. Yes. The mean is 0.92 minus 0.89 equals 0.03 . A No. The mean is 0.92+0.892=0.905. No. The mean is the fraction 0.92 plus 0.89 over 2 equals 0.905 . B No. The mean is 0.92−0.892=0.015. No. The mean is the fraction 0.92 minus 0.89 over 2 equals 0.015 . C No. The mean is 0.90+0.852=0.875. No. The mean is the fraction 0.90 plus 0.85 over 2 equals 0.875 . D No. The mean is 0.90−0.85=0.05.