Question

the acceptable level for insect filth in a certain food item is 5 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. a simple random sample of 40 ten - gram portions of the food item is obtained and results in a sample mean of ( \bar{x}=5.4 ) insect fragments per ten - gram portion. complete parts (a) through (c) below
(c) what is the probability a simple random sample of 40 ten - gram portions of the food item results in a mean of at least 5.4 insect fragments?
( p(\bar{x}geq5.4)=0.1292 ) (round to four decimal places as needed )
is this result unusual?
a. this result is not unusual because its probability is small.
b. this result is unusual because its probability is large.
c. this result is not unusual because its probability is large.
d. this result is unusual because its probability is small.
what might we conclude?
a. since this result is not unusual, it is reasonable to conclude that the population mean is higher than 5.
b. since this result is unusual, it is reasonable to conclude that the population mean is higher than 5.
c. since this result is unusual, it is not reasonable to conclude that the population mean is higher than 5.
d. since this result is not unusual, it is not reasonable to conclude that the population mean is higher than 5.

Explanation:

In statistics, an event is considered unusual if its probability is less than or equal to \(0.05\). Here, \(P(\bar{x}\geq5.4) = 0.1292>0.05\), so the result is not unusual. If the result is not unusual, it could be due to random sampling variation and not necessarily because the population mean is higher than \(5\).

Answer:

C. This result is not unusual because its probability is large.
A. Since this result is not unusual, it is reasonable to conclude that the population mean is higher than 5.