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sveticcg
12 days ago
8

According to an article in marketing news, fewer checks are being written at grocery store checkout stands than in the past. to

determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. check written year 1 year 2 year 3 yes 225 175 125 no 275 325 375 referring to table above, the expected number of shoppers who pay by check in year 1 if there is no difference in the proportion of shoppers who pay by check among the three years is
Business
1 answer:
stepan [3K]12 days ago
8 0
<span>Provided:
Payments made by check       Year 1    Year 2    Year 3
Yes:     225           175        125
No:      275           325        375


</span><span>If the proportion of shoppers paying by check remained unchanged among the three years, the anticipated number of shoppers who pay by check in year 1 is 175.

Each year records 500 customers, and the percentage of customers paying by check diminished from 45% to 25%. Assuming constant proportions, I interpreted the data as an average. Therefore, (225+175+125) / 3 = 525 / 3 = 175.</span>
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Utilizing Chebyshev’s Theorem is key.

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According to Chebyshev’s Theorem, at least 1−1/k² of the data is within k standard deviations from the mean. Setting k = 4 gives us:

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