In a random sample of 18 families, the average weekly food expense was $95.60 with a sample standard deviation of $22.50. Determine whether a normal distribution (Z values) or a t- distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of weekly food expense is normally shaped.

t-distribution should be used to construct a confidence interval.

Step-by-step explanation:

We are given that a random sample of 18 families, the average weekly food expense was $95.60 with a sample standard deviation of $22.50.

We have to determine whether a normal distribution (Z values) or a t- distribution should be used or whether neither of these can be used to construct a confidence interval.

Since in this question we are provided with;

Sample average weekly food expense, = $95.60

Sample standard deviation, s = $22.50

Sample of families, n = 18

The distribution that we will use here to construct a confidence interval will be t-distribution because in the question we don't know anything about population standard deviation .

Normal distribution is used when we know population standard deviation .

So, the pivotal quantity for confidence interval that will be used is One-sample t-test statistics;

                P.Q. = ~

Therefore, t-distribution should be used to construct a confidence interval.

A function from a set to a set is a relation that assigns to each element in the set exactly one element in the set . The set is the domain (also called the set of inputs) of the function and the set contains the range (also called the set of outputs).

.

We have the following equation:

That can be written as:

Recall that the definition of exponential functions establishes that:

.

That is:

In this problem, , therefore this is not an exponential function.

The function:

is an exponential function because is a function of the form

So . Since and being raised to the power of , the function increases. This means that increases as increases as illustrated in Figure 1. This represents a growth.

The function:

can be written as:

and is an exponential function because is a function of the form

So . Since and being raised to the power of , the function increases. As in the previous exercise, this means that increases as increases as illustrated in Figure 2. This represents a growth.

The function:

is an exponential function because is a function of the form

So . Since and being raised to the power of , the function decreases. Here this means that decreases as increases as illustrated in Figure 3. This represents a decay.

The function:

is an exponential function because is a function of the form

So . Since and being raised to the power of , the function increases. So in this function also increases as increases as illustrated in Figure 4. This represents a growth.