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Answer:
There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.
Step-by-step explanation:
To solve this problem, we run a hypothesis test about the population proportion.
Proportion in the null hypothesis (p0) = 0.2
Sample size (n) = 75
Sample proportion (sp) = 24/75 = 0.32
Significance level = 0.01
H0: p = 0.2
Ha: p 0.2
Test statistic = (sp - p0) / sqrt ((p0) (1-p0) / n)
Left critical Z value (for 0.01) = -2.5758
Right critical Z value (for 0.01) = 2.5758
Calculated statistic = (0.32 - 0.2) / sqrt ((0.32) (1-0.32) / 75) = 2.2278
Since, -2.5758 < Test statistic < 2.5758, the null hypothesis cannot be rejected. There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.