In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-cigarette) in the past week. This means that $n = 1186, \pi = \frac{248}{1186} = 0.2091$

Construct a 90% confidence interval to estimate the population proportion of Americans age 18-29 who vaped in the past week.

So $\alpha = 0.10$ , z is the value of Z that has a pvalue of $1 - \frac{0.10}{2} = 0.95$ , so $z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 - 1.645\sqrt{\frac{0.2091*0.7909}{1186}} = 0.1897$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 + 1.645\sqrt{\frac{0.2091*0.7909}= 0.2285$

The 90% confidence interval is (0.1897, 0.2285).

3 0

3 years ago

Find the surface area and volume of a sphere with a radius r = 0.8 ft. Round your answer to the nearest tenth. A. 7.8 ft2; 2.6 f

fiasKO [112]

Surface area of a sphere = 4πr²

Surface area of the sphere = 4π(0.8)² = 8.0 ft²

Volume of a sphere = 4/3 πr³

Volume of the sphere = 4/3 π(0.8)³ = 2.1 ft³

Answer: Surface area = 8.0 ft² and volume - 2.1 ft³ (Answer C)

7 0

2 years ago

Two slits are illuminated by a 348 nm light. The angle between the zeroth-order bright band at the center of the screen and the

Andre45 [30]

Answer:0.369 m

Step-by-step explanation:

Given

Distance between slit and screen is $D=154 cm$