Question

Suppose the marketing company did do a survey. They randomly surveyed $200$households and found that in $120$of them, the woman made the majority of the purchasing decisions. We are interested in the population proportion of households where women make the majority of the purchasing decisions.

Identify the following:

a. $x=$ ______

b. $n=$ ______

c. $p\prime =$ ______

Short answer

The value of

a). $x=120$

b). $n=200$

c).$p\text{'}=0.6$

Step-by-step solution

Part (a) Step 1: Given Information

They randomly surveyed $200$households and found that in $120$ of them.

Part (a) Step 2: Explanation 

The number of successes is$x=120$.

Part (b) Step 1: Given Information

They randomly surveyed $200$households and found that in $120$ of them.

Explanation(Part b)

According to the information, The number of randomly surveyed households is 200.

We can consider n as the sample size.

Therefore, the sample size is $n=200$households.

Part (c) Step 1: Given Information 

They randomly surveyed $200$households and found that in $120$of them.

Part (c) Step 2: Explanation 

The point estimate for the true population proportion is

$$\begin{gathered} p^{\text{'}}=\frac{x}{n} \\ =\frac{120}{200} \\ =0.6 \end{gathered}$$.