Question

a. in a study of 125 tourists, 45 like to travel to paris. find p(hat) and q(hat)
b. in a study of 60 american households, 11 live with an income above $145,000. p(hat) and q(hat)

Explanation:

Step1: Calculate $\hat{p}$ for part a

The formula for $\hat{p}$ is $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes and $n$ is the sample size. For part a, $x = 45$ and $n=125$. So, $\hat{p}=\frac{45}{125}=\frac{9}{25}=0.36$

Step2: Calculate $\hat{q}$ for part a

The formula for $\hat{q}$ is $\hat{q}=1 - \hat{p}$. Since $\hat{p}=0.36$, then $\hat{q}=1 - 0.36 = 0.64$

Step3: Calculate $\hat{p}$ for part b

For part b, $x = 11$ and $n = 60$. Using the formula $\hat{p}=\frac{x}{n}$, we have $\hat{p}=\frac{11}{60}\approx0.183$

Step4: Calculate $\hat{q}$ for part b

Using the formula $\hat{q}=1-\hat{p}$, with $\hat{p}=\frac{11}{60}$, then $\hat{q}=1-\frac{11}{60}=\frac{60 - 11}{60}=\frac{49}{60}\approx0.817$

Answer:

a. $\hat{p}=0.36$, $\hat{q}=0.64$
b. $\hat{p}\approx0.183$, $\hat{q}\approx0.817$