How many more students ate breakfast than skipped breakfast?

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

90% confidence level, hence $\alpha = 0.9$ , z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$ , so $z = 1.645$ .

Item a:

The estimate is $\pi = 0.213 - 0.195 = 0.018$ .

The sample size is n for which M = 0.03, hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}$

$\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2$

$n = 53.1$

Rounding up, a sample size of 54 is needed.

Item b:

No prior estimate, hence $\pi = 0.05$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2$

$n = 751.7$

Rounding up, a sample of 752 should be taken.

A similar problem is given at brainly.com/question/25694087

5 0

3 years ago

Help me please. ------------------------------------------------

ladessa [460]

Answer:

Alicia

Step-by-step explanation:

First, convert the mixed fractions into improper fractions

Alicia

Distance: 5 1/2 = 11/2 = 5.5 miles

Time: 1 2/5 = 7/5 = 1.4 hours

Carlos

Distance: 8 1/8 = 65/8 = 8.125 miles

Time: 2 1/2 = 5/2 = 2.5 hours

Henry

Distance: 3 2/3 = 11/3 = 3.6 reoccuring miles

Time: 1 1/10 = 11/10 = 1.1 hours

Zoe

Distance: 4 2/3 = 14/3 = 4.6 reoccuring miles

Time: 1 3/10 = 13/10 = 1.3 hours

After that, divide the distance by the time

Alicia = 5.5 / 1.4 = 3.93 ( 3 s.f )

Carlos = 8.125 / 2.5 = 3.25

Henry = 3.6 re / 1.1 = 3.3 reoccuring

Zoe = 4.6 / 1.3 = 3.54 ( 3 s.f )

Looking at these answers, we determine which rate is the greatest

Alicia = 3.93

Carlos = 3.25

Henry = 3.3 re

Zoe = 3.54

Alicia hiked the highest rate.

5 0

3 years ago

Write an equation the sum of two times a number and 5 is 11

podryga [215]

5+2x=11 (this is the equation)
-5 -5 
2x=6 (this is the answer)
x=3

5 0

3 years ago