Question

An experiment was conducted on 60 University of Texas undergraduates to evaluate taste preferences. On the 60 participants, 25 prefer the taste of instant coffee and 35 prefer the taste of fresh-brewed coffee. If p is the proportion of UT students who prefer fresh-brewed coffee, what is the width of the 95% confidence interval for p?

Answer 1

Answer:

The width of the 95% confidence interval for p is 0.2496

Step-by-step explanation:

Taking into account that the proportion of the students from the sample that prefer the taste of fresh-brewed coffee is calculated as:

p' = 35/60 = 0.5833

Because there are 60 students in the sample and 35 prefer the taste of fresh brewed coffee.

So, the width of the 95% confidence interval for p is calculated as:

$width=2(1.96)\sqrt{\frac{p'(1-p')}{n} }$

Where n is the number of the students in the sample and 1.96 is the z values that satisfy that:

2P(Z>1.96) = 1 - 0.95 = 0.05

Then, replacing p' by 0.5833 and n by 60, we get:

$width=2(1.96)\sqrt{\frac{0.5833(1-0.5833)}{60} }=0.2495$

Finally, the width of the 95% confidence interval for p is 0.2496