The correct option should be C: "The variance of the sampling distribution of the estimator will increase" because the sample size is decreased from 2500 to 1500.
Given information:
The director originally planned to obtain a random sample of 2500 people who purchased the product.
However, because of budget concerns, the sample size will be reduced to 1500 people.
Now, the variance of the sample distribution can be written as,
[tex]\dfrac{\sigma^2}{n}[/tex] where n is the sample size.
So, the variance is inversely proportional to the sample size.
Here, we can conclude that with an increase in sample size, the variance will decrease and vice versa.
Therefore, the correct option should be C: "The variance of the sampling distribution of the estimator will increase" because the sample size is decreased from 2500 to 1500.
For more details, refer to the link:
https://brainly.com/question/7635845
