If 0° < θ< 90°, θ is a/an what angle?

Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The

kifflom [539]

Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

p = sample proportion = 0.54

n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

- The sample data must have been obtained using a random sampling technique.

- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

and n(1-p) ≥ 10

The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Hope this Helps!!!

8 0

3 years ago

Is ABC DEF? If so, name which similarity postulate or theorem applies. Pls explain. Thanks!! :)

Inessa05 [86]

Answer: B. Similar - AA

Step-by-step explanation:

The AA or Angle-Angle postulate states that if two corresponding angles are congruent, then the triangles are congruent.

3 0

3 years ago

Subtract 8-4 1/2. A. 3 B. 4 C. 4 1/2 D. 3 1/2

Leokris [45]

1.
An expression of the form $a \frac{b}{c}$ is called a "compound fraction"

Compound fractions can be written as simple fractions by multiplying c to a, and then adding the product to c as follows:

$a \frac{b}{c}= \frac{c.a+b}{c}$

for example,

$4\frac{1}{2}$ can be written as:

$4\frac{1}{2}= \frac{2.4+1}{2}=\frac{9}{2}$

2.

when we subtract or add a fraction $\frac{m}{n}$ from an integer k,

we first write k as a fraction with denominator n. We can do this as follows:

$k=k. \frac{n}{n}= \frac{kn}{n}$

for example, if we want to subtract $\frac{9}{2}$ from 8,

we first write 8 as a fraction with denominator 2:

$8=8. \frac{2}{2}= \frac{8.2}{2}= \frac{16}{2}$

3.

Thus,

$8-4 \frac{1}{2}= \frac{16}{2}- \frac{9}{2}= \frac{16-9}{2}= \frac{7}{2}$

4.

The simple fraction 7/2 is not an option, so we write it as a compound fraction as follows:

$\frac{7}{2}= \frac{6+1}{2}= \frac{6}{2}+ \frac{1}{2}=3+ \frac{1}{2}=3\frac{1}{2}$

(So write 7 as the sum of the largest multiple of 2, smaller than 7 + what is left. In our case these numbers are 6 and 1, then proceed as shown)

5. Answer: D

3 0

3 years ago

Read 2 more answers

Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is “nor

Olenka [21]

Answer:

He have <u>47</u> ducks and <u>7</u> cows.

Step-by-step explanation:

Given:

Farmer Jones raises ducks and cows.

He looks out his window and sees 54 animals with a total of 122 feet.

Now, to find the each type of animal he have.