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Finding Significant Difference and P-Value

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More shoppers do their majority of grocery shopping on Saturday than any other day of the week. However, is the day of the week a person does the majority of grocery shopping dependent on age? A study cross-classified grocery shoppers by age and major shopping day ("Major Shopping by Day ," Progressive Grocer Annual Report, April 30, 2002). The data were reported as percentages and no sample sizes were given.

AGE
Major Shopping Day Under 35 35-54 Over 54
Saturday 24% 28% 12%
A day other than Saturday 76% 72% 88%
Source: Extracted from "Major Shopping Day," Progressive Grocer Annual Report, April 30, 2002.

Assume that 200 shoppers for each age category were surveyed.

a. Is there evidence of a significant difference among the age groups with respect to major grocery shopping day? (Use p = 0.05.)
b. Determine the p-value in (a) and interpret its meaning.

See attached file for full problem description.

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This solution provides detailed explanations for questions involving finding significant difference and p-value.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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