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Scheherazade (Sche) is studying the effects of the pandemic on her neighborhood, Manzanita Park. In her research, she has found that the mean household income for January of 2021 is $890 less than it was in January of 2020. The median decrease was $743 and the standard deviation of the decrease was $234.
a. If an additional household was included that had lost $900 in their January income, what effect would that have on the mean of the lost incomes? What would happen to the standard deviation of lost incomes? What would be the effect on the median of lost incomes?
b. If the Manzanita Park Development Council had given out a relief payment of $150 to EACH household in the neighborhood in January, what would the mean, median and standard deviation of the lost incomes have been?
c. If Sche collects a simple random sample of 43 households from the neighborhood, what is the probability that the mean lost income for the month of January in this sample would exceed $900?
d. What assumption is necessary to perform the calculations in part c?
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