Explain how you can use a model to find 6 x17

A certain article indicates that in a sample of 1,000 dog owners, 610 said that they take more pictures of their dog than of the

lbvjy [14]

Answer:

(a) The 90% confidence interval is: (0.60, 0.63) Correct interpretation is (3).

(b) The 95% confidence interval is: (0.42, 0.46) Correct interpretation is (1).

(c) First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

Step-by-step explanation:

(a)

Let X = number of dog owners who take more pictures of their dog than of their significant others or friends.

Given:

X = 610

n = 1000

Confidence level = 90%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{610}{1000}=0.61$

The critical value of z for a 90% confidence level is:

$z_{\alpha/2}=z_{0.10/2}=z_[0.05}=1.645$

Construct a 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.61\pm 1.645\sqrt{\frac{0.61(1-0.61}{1000}}\\=0.61\pm 0.015\\=(0.595, 0.625)\\\approx(0.60, 0.63)$

Thus, the 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends is (0.60, 0.63).

Interpretation:

There is a 90% chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within the interval (0.60, 0.63).

Correct option is (3).

(b)

Let X = number of dog owners who are more likely to complain to their dog than to a friend.

Given:

X = 440

n = 1000

Confidence level = 95%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{440}{1000}=0.44$

The critical value of z for a 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Construct a 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.44\pm 1.96\sqrt{\frac{0.44(1-0.44}{1000}}\\=0.44\pm 0.016\\=(0.424, 0.456)\\\approx(0.42, 0.46)$

Thus, the 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend is (0.42, 0.46).

Interpretation:

There is a 95% chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within the interval (0.42, 0.46).

Correct option is (1).

(c)

The confidence interval in part (b) is wider than the confidence interval in part (a).

The width of the interval is affected by:

The confidence level
Sample size
Standard deviation.

The confidence level in part (b) is more than that in part (a).

Because of this the critical value of z in part (b) is more than that in part (a).

Also the margin of error in part (b) is 0.016 which is more than the margin of error in part (a), 0.015.

First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

4 0

3 years ago

Using Parallel Lines Find m 1 and m 2. Explain your reasoning.

Molodets [167]

i don't know if there is a graph for this problem, but m1 should always equal m2

if m1 and m2 are parallel, one line that is perpendicular to m1 is always perpendicular to m2, and the slopes of m1 and m2 are equal and their lines should never intersect

8 0

3 years ago

there are 6 times as many dogs as cAts. if tje total number of dogs and cats is 21 how many dogs are tjrre

frez [133]

There are 18 dogs. You do 21/7.

5 0

3 years ago

Find the volume of the sphere with a radius, r, of 3/2 feet and π ≈ 3.14.

nalin [4]

Answer:

V= 14.13

Step-by-step explanation:

Information needed:

V= 4/3 $\pi$ r^3

$\pi$ = 3.14

r= 3/2

Solve:

V= 4/3 $\pi$ r^3

V= 4/3(3.14)(3/2)^3

V= 4/3(3.14)(27/8)

V= 14.13

3 0

3 years ago

Read 2 more answers

a cup is 6.4 cm tall, not including the 0.6 cm lip. cups are stacked inside one another. select the function that represents the

Alja [10]

Answer: 20

H(c) = 6.4 + 0.6c

6.4 is the constant.

When the height of the cups is 18.4 the function is:

18.4 = 6.4 + 0.6c

Then, you add 6.4 from both sides

18.4 - 6.4 + 6.4 = 6.4 + 0.6c - 6.4 + 6.4

Simplify

18.4 = 6.4 + 0.6c

Switch sides

6.4 + 0.6c = 18.4

Multiply both sides by 10

6.4 x 10 + 0.6c x 10 = 18.4 x 10

Refine

64 + 6c = 184

Subtract 64 from both sides

64 + 6c - 64 = 184 - 64

Simplify

6c = 120

Divide both sides by 6

6c/6 = 120/6

c = 20

8 0

3 years ago