c) A machine packages shirt in bags with a mean weight of 3 kg. A random sample of 20 bags
has a mean weight of 3.05 kg with a standard deviation of 0.05kg, From the data given, state the
value of a
(i) parameter [1]
(ii) statistic
To determine the value of parameter 'a' and statistic, we first need to understand the difference between them. In statistics, a parameter represents a numerical value that describes a population, while a statistic represents a numerical value that describes a sample.
In this scenario, the population consists of all the bags that the machine packages. We are given a random sample of 20 bags, which allows us to estimate the parameters of the population.
(i) Parameter:
The parameter we are interested in is the mean weight of the bags in the population. We are told that the mean weight of the bags in the population is 3 kg. Therefore, the value of the parameter 'a' is 3 kg.
(ii) Statistic:
The statistic we can calculate from the sample is the mean weight of the bags in the sample. We are given that the mean weight of the 20 bags in the sample is 3.05 kg. Hence, the value of the statistic is 3.05 kg.
To summarize:
(i) Parameter 'a' = 3 kg
(ii) Statistic = 3.05 kg