Question

The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg. let

denote the proportion of all cartons which have at least one broken egg. Which of the following calculates the point estimate for p and also the critical value for the 90% confidence interval for p?

Answer 1

To calculate the point estimate for p, we divide the number of cartons with at least one broken egg by the total number of cartons in the sample:

Point estimate for p = Number of cartons with at least one broken egg / Total number of cartons in the sample = 30 / 250

To calculate the critical value for the 90% confidence interval for p, we need to use a statistical table or calculator specific to the desired confidence level. The critical value represents the number of standard errors away from the mean we need to consider for constructing the confidence interval. Without the specific values, I am unable to provide the exact critical value.

However, for a 90% confidence interval, the critical value can be determined using a standard normal distribution (Z-distribution) or a t-distribution depending on the sample size and distribution assumptions.