Question

A consumer group is investigating two brands of popcorn, R and S. The percent of kernels that will pop for the population of kernels in Brand R is 90% (PK - 0.90). The percent of kernels that will pop for the population of kernels in Brand S is 85% (ps = 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
Brands 200 0.89

Consider the sampling distribution for the difference in all samples of size 100 kernels from Brand Rand 200 kernels from Brand S (Brand R - Brand S). A consumer group claims that the difference in proportions has a mean of 0.03. Is this correct?

Answer 1

The consumer group's claim that the difference in proportions has a mean of 0.03 is incorrect

How to calculate the difference in proportion

The table entries are given as:

              Kernels    Proportion that Popped

Brand R   100          0.92

Brand S   200          0.89

The proportions of the samples that will pop for both brands are given as:

$P_k = 0.90$

$P_s = 0.85$

Calculate the difference of both proportions

$d =P_k - P_s$

So, we have:

$d =0.90 - 0.85$

$d =0.05$

This means that:

The difference in proportions has a mean of 0.05

Hence, the claim of the consumer group is incorrect

Read more about sample proportions at:

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