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?

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MrRoyal MrRoyal · Answer 1 · 2022-01-26T06:29:42+01:00

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

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:

[tex]P_k = 0.90[/tex]

[tex]P_s = 0.85[/tex]

Calculate the difference of both proportions

[tex]d =P_k - P_s[/tex]

So, we have:

[tex]d =0.90 - 0.85[/tex]

[tex]d =0.05[/tex]

This means that:

The difference in proportions has a mean of 0.05

Hence, the claim of the consumer group is incorrect

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