MATHEMATICS COLLEGE

In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the proportion of all students who read or watch the news on a daily basis. Interpret your results. If you wanted to develop a 95% confidence interval with a margin of error of .01, how many students would need to be surveyed?

Answers

Answer 1

Answer:

The 90% confidence interval is $0.199 < p < 0.261$

The sample size to develop a 95% confidence interval is $n = 2032$

Step-by-step explanation:

From the question we are told that

The sample size is n =500

The sample proportion is $\^ p = 0.23$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $(\alpha )/(2)$ is

$Z_{(\alpha )/(2) } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{(\alpha )/(2) } * \sqrt{(\^ p (1- \^ p))/(n) }$

=> $E = 1.645 * \sqrt{(0.23 (1- 0.23))/(500) }$

=> $E = 0.03096$

Generally 90% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.23 -0.03096 < p < 0.23 + 0.03096$

=> $0.199 < p < 0.261$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $(\alpha )/(2)$ is

$Z_{(\alpha )/(2) } = 1.96$

The margin of error is given as $E = 0.01$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{(\alpha )/(2) }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [(1.96 )/(0.01) ]^2 *0.23 (1 - 0.23 )$

=> $n = 2032$

Related Questions

Karen earns $54.60 for working 6 hours. If the amount she earns varies directly with thenumber of hours she works, how many hours would she need to work to earn anadditional $260?
Charlie is 4 feet 11 inches tall. If there are 2.54 centimeters in 1 inch, what is Charlie’s height in centimeters?
Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300) y-intercept, b0 = Slope, b1 = MSE = One of OSH’s goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal?
A certain test preparation course is designed to help students improve their scores on the MCAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 6 students' scores on the exam after completing the course: 19, 15, 9, 17, 7, 16. Using these data, construct a 95% confidence interval for the average net change in a students's score after completing the course. Assume the population is approx. normal.Step 1. calculate the sample mean for the given sample data (round answer to 1 decimal place)Step 2. Calculate the sample standard deviation for the given sample data ( round answer to 1 decimal place)Step 3. Find the critical value that should be used in constructing the confidence interval. ( round answer to 3 decimal placed)Step 4. construct the 95% confidence interval (round answer to 1 decimal place)
What is the sum of 18 23/30+ 2/3

You are trying to determine if you should accept a shipment of eggs for a local grocery store. About 4% of all cartons which are shipped have had an egg crack while traveling. You are instructed to accept the shipment if no more than 10 cartons out of the 300 you inspect have cracked eggs. What is the probability that you accept the shipment? (In other words, what is the probability that, at the most, you had 16 cartons with cracked eggs?)a. 1012.
b. 3669.
c. 5319.
d. 4681.
e. 5832.
f. 6331.

Answers

Answer:

0.8809

Step-by-step explanation:

Given that:

The population proportion p = 4% = 4/100 = 0.04

Sample mean x = 16

The sample size n = 300

The sample proportion $\hat p =(x)/(n)$

= 16/300

= 0.0533

∴

$P(\hat p \leq 0.0533) = P\bigg ( \frac{\hat p - p}{\sqrt{(P(1-P))/(n)}}\leq\frac{0.0533 - 0.04}{\sqrt{(0.04(1-0.04))/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{(0.04(0.96))/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{(0.0384)/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{1.28 * 10^(-4)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq(0.0133)/(0.0113)}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq1.18}\bigg )$

From the z tables;

= 0.8809

Let X be the random variation that follows a normal distribution;

Then;

population mean $\mu$ = n × p

population mean $\mu$ = 300 × 0.04

population mean $\mu$ = 12

The standard deviation $\sigma = √(np(1-p))$

The standard deviation $\sigma = √(300 * 0.04(1-0.04))$

The standard deviation $\sigma = √(11.52)$

The standard deviation $\sigma = 3.39$

The z -score can be computed as:

$z = (x - \mu)/(\sigma)$

$z = (16 -12)/(3.39)$

$z = (4)/(3.39)$

z = 1.18

The required probability is:

P(X ≤ 10) = Pr (z ≤ 1.18)

= 0.8809

I need helpppp
plsssanyoneee

Answers

Answer:

$x^(6)$ / $z^(-1)$

Step-by-step explanation:

Which function describes this table of values?X Y
10 8
5 4
0 0
-5 -5

Answers

Answer:

which function describes this table of values x y 0 0

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle

Answers

Answer:

18√2

Step-by-step explanation:

The area of the smaller triangle is 1/2 that of the larger one. Since the triangles are similar, the dimensions of the smaller triangle are √(1/2) those of the larger one.

36 · √(1/2) = 36 · (√2)/2 = 18√2 . . . . length of line dividing the triangle

Writing Describe another methodfor solving the expression in
Exercise 1. Does this method always
work? Explain.

Answers

Answer: pontos livres

Step-by-step explanation:

o cachorrinho wwss veyry rápido

Will give 100 points to anyone who can find the arc measure and show work! thanks!

Answers

Answer:

2π/3 radians

----------------------

Given:

Arc length (s) = 8π/3
Radius (r) = 4 km

To find the arc measure (θ) in radians, we can use the formula:

s = rθ

Now, plug in the given values:

8π/3 = 4θ

To solve for θ, divide both sides by 4:

(8π/3) / 4 = θ

Simplify the expression:

2π/3 = θ

So, the arc measure (θ) is 2π/3 radians

Other Questions

Jake buys a gaming system and equipment for $2200.00 with a credit card that has a 28% APR. He makes a $100.00 monthly payment. What is the total amount of interest based on the APR? Enter your answer as a dollar amountsuch as: $324.

A traveler has 8 pieces of luggage. How many ways can he select 4 pieces of luggage for a trip

Wat does PAYE stands for?

A house and a lot are appraised at 212,400. If the value of the house is five times the value of the lot, how much Is the house worth