A random sample of 84 shoppers were interviewed and 51 said they prefer to shop alone rather than with someone else. Let p represent the proportion of all shoppers at this mall who would prefer to shop alone. Find a point estimate (p hat) for p.
To find the point estimate (p hat) for proportion, we use the formula:
p hat = x / n
Where:
x = number of shoppers in the sample who prefer to shop alone
n = total number of shoppers in the sample
In this case, x = 51 (since 51 shoppers said they prefer to shop alone) and n = 84 (the total number of shoppers interviewed).
So, the point estimate (p hat) for proportion (p) would be:
p hat = 51 / 84
Calculating this, we get:
p hat ≈ 0.607 (rounded to three decimal places)
Therefore, the point estimate (p hat) for the proportion of all shoppers at this mall who would prefer to shop alone is approximately 0.607.