Kyle ran the 200 yard dash in 50 seconds how many feet could kyle run each second

A magazine provided results from a poll of 500500 adults who were asked to identify their favorite pie. Among the 500500 respon

Komok [63]

Answer:

99% confidence interval is wider as compared to the 80% confidence interval.

Step-by-step explanation:

We are given that a magazine provided results from a poll of 500 adults who were asked to identify their favorite pie.

Among the 500 respondents, 14% chose chocolate pie, and the margin of error was given as plus or minus ±3 percentage points.

The pivotal quantity for the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who chose chocolate pie = 14%

n = sample of adults = 500

p = true proportion

Now, the 99% confidence interval for p = $\hat p \pm Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

Here, $\alpha$ = 1% so $(\frac{\alpha}{2})$ = 0.5%. So, the critical value of z at 0.5% significance level is 2.5758.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.03 for 99% interval.

So, 99% confidence interval for p = $0.14 \pm2.5758 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

= [0.14 - 0.03 , 0.14 + 0.03]

= [0.11 , 0.17]

Similarly, 80% confidence interval for p = $0.14 \pm 1.2816 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

Here, $\alpha$ = 20% so $(\frac{\alpha}{2})$ = 10%. So, the critical value of z at 10% significance level is 1.2816.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.02 for 80% interval.

So, 80% confidence interval for p = [0.14 - 0.02 , 0.14 + 0.02]

= [0.12 , 0.16]

Now, as we can clearly see that 99% confidence interval is wider as compared to 80% confidence interval. This is because more the confidence level wider is the confidence interval and we are more confident about true population parameter.

5 0

3 years ago

Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irr

Colt1911 [192]

Answer:

Rational numbers are fractional numbers, whose numerator and denominator are integers and the denominator is ever zero.

Step-by-step explanation:

The sum of rational numbers gives a rational number;

$\frac{1}{3}$ + $\frac{1}{3}$ = $\frac{2}{3}$ , because the evaluation of the denominator always results to a non-zero integer.

The product of $\frac{1}{3}$ x $\frac{1}{3}$ = $\frac{1}{9}$ , which multiply both numerator and denominator to give integer numbers.

The sum and product of rational and irrational numbers are always irrational numbers, for instance,

$\frac{1}{3}$ x 7 = 2.3 , which is a number which decimal points that can only be represented by the product irrational number and rational number , where 7 is an irrational number.

$\frac{1}{3}$ + 7 = 7 $\frac{1}{3}$ , which is a whole number and fractional number combined.

4 0

3 years ago

Alice has 12 more trees in her garden than Stephen has. After Stephen planted 10 more trees and Alice dug out 4, together they h

Dafna1 [17]

Answer:

Stephen has 9 trees

Alice has 21 trees

Step-by-step explanation:

At the beginning:

Stephen = x trees

Alice = x + 12 trees

At the end:

Alice = (x + 12) - 4 trees

Stephen = x + 10 trees

Total = 36

Then

$((x+12)-4)+(x+10)=36\\ \\(x+12-4)+(x+10)=36\\ \\(x+8)+(x+10)=36\\ \\x+8+x+10=36\\ \\2x+18=36\\ \\2x+18-18=36-18\\ \\2x=18\\ \\x=9$

Stephen - 9 trees

Alice - 9 + 12 = 21 trees

8 0

3 years ago

Read 2 more answers

The cost to rent a construction crane is $1200 per day plus $150 per oh use. Your budget for one-day crane rental is a most $360

Komok [63]

1200 + 150 = 1350 (if one day and one use)

Budget is 3600

We can use the crane 16 times

Explanation:

Budget is 3600 and 1200 + 150 (16) = 3600

6 0

3 years ago

PLZ HELP I WILL GIVE BRAINLYEST AND 100 POINTS IF YOUR CORRECT

Sav [38]

Answer:

3

Step-by-step explanation:

i double checked

4 0

2 years ago

Read 2 more answers