a food delivery service manager would like to estimate the mean amount of time it takes employees of his…

a food delivery service manager would like to estimate the mean amount of time it takes employees of his company to deliver food to the customers. to do so, he selects a random sample of 10 deliveries from the large number of deliveries made and records the amount of time each of those deliveries took. are the conditions for constructing a t confidence interval met?\nno, the random condition is not met.\nno, the 10% condition is not met.\nno, the normal/large sample condition is not met.\nyes, the conditions for inference are met.

a food delivery service manager would like to estimate the mean amount of time it takes employees of his company to deliver food to the customers. to do so, he selects a random sample of 10 deliveries from the large number of deliveries made and records the amount of time each of those deliveries took. are the conditions for constructing a t confidence interval met?\nno, the random condition is not met.\nno, the 10% condition is not met.\nno, the normal/large sample condition is not met.\nyes, the conditions for inference are met.

Answer

Explanation:

Step1: Check the random condition

The manager selects a random sample of 10 deliveries. So the random condition is met.

Step2: Check the 10% condition

Since there is a large number of deliveries made (the population is large), (10) deliveries (the sample size (n = 10)) is less than (10%) of the population. So the 10% condition is met.

Step3: Check the Normal/large - sample condition

For a (t) - confidence interval, when (n<30), we need to check if the data come from a normal distribution. But we have no information about the distribution of delivery times. However, if we assume that the population of delivery times is normal (or approximately normal), the (t) - confidence interval can be constructed. In the absence of information suggesting non - normality and given that the problem is presented in a basic statistics context (where for small samples in the absence of evidence to the contrary, we assume the population is normal for (t) - interval construction), we consider the conditions for constructing a (t) confidence interval.

Answer:

Yes, the conditions for inference are met.