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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

Please help 8th grade math

Zepler [3.9K]

Answer:

1500 calories

Step-by-step explanation:

2400 is 100% of in this case, 8/8

So then we know that 1/8 of 2400 is 300 because we just divide it by 8. Sarah eats 5/8 that much so we multiply 300 by 5 which gives us 1500

6 0

3 years ago

Read 2 more answers

Put these numbers in order from greatest to least. 4,-6/10 ,10/25,11/22

Fiesta28 [93]

Answer:

-6/10, 10/25,11/22,4.

Step-by-step explanation:

negatives are always the lowest

6 0

3 years ago

A parallel system functions whenever at least one of its components works. Consider a parallel system of 5 components, and suppo

Aneli [31]

Answer:

Probability that component 4 works given that the system is functioning = 0.434 .

Step-by-step explanation:

We are given that a parallel system functions whenever at least one of its components works.

There are parallel system of 5 components and each component works independently with probability 0.4 .

Let A = Probability of component 4 working properly, P(A) = 0.4 .

Also let S = Probability that system is functioning for whole 5 components, P(S)

Now, the conditional probability that component 4 works given that the system is functioning is given by P(A/S) ;

P(A/S) = {Means P(component 4 working and system also working)

divided by P(system is functioning)}

P(A/S) = {In numerator it is P(component 4 working) and in

denominator it is P(system working) = 1 - P(system is not working)}

Since we know that P(system not working) means that none of the components is working in system and it is given with the probability of 0.6 and since there are total of 5 components so P(system working) = 1 - $0.6^{5}$ .

Hence, P(A/S) = $\frac{0.4}{1 - 0.6^{5} }$ = 0.434.

7 0

3 years ago

A food manufacturer stores corn oil in a right circular cylindrical container. This container has a height of 12 inches, and a b

Akimi4 [234]

This is not a quiestion but the area of this shape is 401.92inches. A=2πrh+2πr2

8 0

3 years ago