Benjamin believes that ¼ % is equivalent to 25%. Is he correct? Why or Why not?

in a random sample of 200 people, 154 said that they watched educational television. fine the 90% confidence interval of the tru

melisa1 [442]

Answer:

[0.7210,0.8189] = [72.10%, 81.89%]

Step-by-step explanation:

The sample size is

n = 200

the proportion is

p = 154/200 = 0.77

Since both np ≥ 10 and n(1-p) ≥ 10

We can approximate this discrete binomial distribution with the continuous Normal distribution. As the sample size is large enough, not applying the continuity correction factor makes no significant difference.

The approximation would be to a Normal curve with this parameters:

Mean

p = 0.77

Standard deviation

$\bf s=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.77*0.23}{200}}=0.0298$

The 90% confidence interval for the proportion would be then

$\bf [0.77-z^*0.0298, 0.77+z^*0.0298]$

where $\bf z^*$ is the 10% critical value for the Normal N(0,1) distribution , this is a value such that the area under the N(0,1) curve outside the interval $\bf [-z^*,z^*]$ is 10%=0.1

We can either use a table, a calculator or a spreadsheet to get this value.

In Excel or OpenOffice Calc we use the function

NORMSINV(0.95) and we get a value of 1.645

The 90% confidence interval for the proportion is then

$\bf [0.77-1.645^*0.0298, 0.77+1.645^*0.0298]=[0.7210,0.8189]$

This means there is a 90% probability that the proportion of people who watch educational television is between 72.10% and 81.89%

If the television company wanted to publicize the proportion of viewers, do you think it should use the 90% confidence interval?

Yes, I do.

5 0

2 years ago

1. which angle is congruent to Angle 1?

Inessa [10]

Part 1) which angle is congruent to Angle 1?

we know that

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles

m∠5=m∠1 ----------> by corresponding angles postulate

therefore

the answer Part 1) is

Angle $5$

Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?

we know that

Alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.

in this problem

m∠1=m∠8 -------> by alternate exterior angles theorem

therefore

the answer part 2) is the option

Alternate Exterior Angles Theorem

Part 3) If m Angle 5 = 42 degrees, what is m Angle 4?

we know that

Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal

m∠4=m∠5 --------> by alternate interior angles theorem

so

m∠4= $42\ degrees$

therefore

the answer Part 3) is

$42\ degrees$

5 0

2 years ago

Read 2 more answers

Mixing two kinds of candy the price of which was $2 and $4 per pound, Ella got a 10-lb mix of candy, which cost $2.90 per pound.

topjm [15]

1. You have the following information given in the problem above:

- Ella mixed two kinds of candy the price of which was $2 and $4 per pound.
- Ella got a 10-lb mix of candy, which cost $2.90 per pound.

2. Therefore, let's call:

x: pounds of the first kind of candy.
y: pounds of the second kind of candy.

3. Then, you have:

2x+4(10-x)=(2.90)(10)

4. When you clear x, you obtain:

2x+40-4x=29
-2x=29-40
x=-11/-2
x=5.5 pounds

x+y=10
y=10-x
y=10-5.5
y=4.5 pounds

8 0

2 years ago

A box of crayons costs $1.75, including tax. Mr. Valentino wants to purchase boxes of crayons for his class and has a $25 budget

Mnenie [13.5K]

Mr. Valentino can`t go over his budget of $25. The amount of money times the amount of boxes needs to be less than or equal to $25:
Answer: A ) $1.75 x ≤ $25,
where x is the amount of boxes he bought.

4 0

2 years ago

Read 2 more answers

Jake went on a riverboat tour. After returning from the tour, he was curious to know the speed at which the boat was going. Duri

atroni [7]

I'm sorry I'm too lazy to read all of that. However, I did get the main point. The river was going at 3 mph. Since he wanted to travel 10 miles upstream and downstream, you would have to subtract 20 by 3. This would mean he was going at a speed of 17 mph.

4 0

2 years ago