A random sample of 84 shoppers were interviewed and 51 said they prefer to shop alone rather than with someone such as friends or family. Let p represent the proportion of all shoppers at this mall who would prefer to shop alone. Find a point estimate for p from the sample proportion.
n=84
x=51
51/84=0.607
p-hat = 0.607
To find a point estimate for p from the sample proportion, we can use the formula:
Point Estimate = Sample Proportion
Given that 51 shoppers out of the random sample of 84 prefer to shop alone, the sample proportion can be calculated as:
Sample Proportion = Number of shoppers who prefer to shop alone / Total number of shoppers
Sample Proportion = 51 / 84
Therefore, the point estimate for p, the proportion of all shoppers at this mall who would prefer to shop alone, is 51/84.
To find a point estimate for p (the proportion of all shoppers at the mall who prefer to shop alone), we can use the sample proportion.
The sample proportion is obtained by taking the number of shoppers in the sample who prefer to shop alone and dividing it by the total number of shoppers in the sample.
In this case, the number of shoppers who prefer to shop alone is 51 out of a sample size of 84 shoppers. Therefore, the sample proportion can be calculated as:
p̂ = (number of shoppers who prefer to shop alone) / (total number of shoppers in the sample)
Substituting the values:
p̂ = 51 / 84
Simplifying:
p̂ ≈ 0.6071
So, the point estimate for p, the proportion of all shoppers at the mall who prefer to shop alone, is approximately 0.6071.