A researcher would like to estimate the mean amount of money the typical American spends on lottery tickets in a month. The researcher would like to estimate the mean with 99% confidence. Which sample size options would yield the smallest margin of error?

Answers

Answer 1

Based on the formula, we can say that the margin of error will be reduced if the sample size is increased.

To obtain the smallest margin of error with 99% confidence, a sample size of 1689 would be needed.

A margin of error refers to the degree of error that may arise due to chance when attempting to estimate a population parameter such as a mean. It is calculated as the product of a critical value, a standard deviation, and a confidence interval, then divided by the square root of the sample size.

N is the sample size, which refers to the number of items included in the sample from the population. A larger sample size would be beneficial since it lowers the margin of error. When the sample size rises, the standard error of the mean decreases, implying that we are more confident in our estimate of the population mean. A smaller margin of error is desirable since it results in a more precise estimate of the population parameter.

The formula for the margin of error is given by:

Margin of Error = (Critical Value) (Standard Deviation) / sqrt(N).

To obtain the smallest margin of error with 99% confidence, a sample size of 1689 would be needed. The formula for the sample size calculation for this scenario is:

N = [(Zα/2)σ / E]²

Where, Zα/2 = 2.58, σ is the standard deviation, and E is the margin of error.

Using Zα/2 = 2.58 for a 99% confidence interval and the smallest possible margin of error to obtain a sample size for which the margin of error is minimized, we have:

N = [(Zα/2)σ / E]² = [(2.58)σ / E]²

Since the goal is to minimize the margin of error, we use the smallest possible value for E:1.

Therefore, N = [(2.58)σ / 1]²2.

Solving for N:

N = 6.6564σ²

To obtain the smallest margin of error with 99% confidence, we must solve for the smallest possible value of N that satisfies the above equation. We obtain:

N = 6.6564σ²

We don't have any information about the standard deviation, σ, in the given question, so we can't solve for N.

However, based on the formula, we can say that the margin of error will be reduced if the sample size is increased.

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Related Questions

В чемпионате мира по футболу участвуют 32 команды. С помощью жребия их делят
на восемь групп, по четыре команды в каждой. Группы называют латинскими буквами от А
до Н. Какова вероятность того, что команда Франции, участвующая в чемпионате, окажется
в одной из групп А, В, С или D?
Ответ:​

Answers

Ответ:​

P = 1/4

Объяснение:

Probability of an event happening = Number of ways it can happen / Total number of outcomes

Number of ways it can happen: 1 (there is only 1 group with french team in it)

Total number of outcomes: 4 (there are 4 groups)

So the probability = 1/4

------------------------------------------------------------------------------------

Вероятность возникновения события = Количество способов которыми это может произойти / Общее количество исходов

Количество способов которыми это может произойти: 1 (есть только 1 группа с французской командой в ней)

Общее количество исходов: 4 (есть 4 группы)

Таким образом вероятность = 1/4

Я надеюсь, что это было полезно ^^

The radius of a circle is 4 feet. What is the area?

r=4ft

Give the exact answer in simplest form.

Answers

Abswer is here

100.571429

A ladder that is 18 ft. long is leaning
against the side of a building. If the angle
formed between the ladder and the ground
is 30°, how far is the bottom of the ladder
from the base of the building?

Answers

it’s cut off, but the bottom side of the triangle is labelled ‘x’
hope this helps!


The price of a cup of coffee was $2.10 yesterday. Today, the price rose to $2.45. Find the percentage increase. Round your answer to the nearest tenth of a
percent.

Answers

Answer:

16.6667% increase

Step-by-step explanation:

Percentage Increase=Final Value−Starting Value|Starting Value|×100  

Answer:

17%

Step-by-step explanation:

The increase is calculated as the difference between yesterday's price and today's price, hence $2.45 - $2.10 = $0.35

As a fraction of yesterday's price, the fraction is [tex]\frac{0.35}{2.10}[/tex], which reduces to [tex]\frac{1}{6}[/tex].  Expressed as a decimal fraction, this is 0.16...  Shift the decimal point two places to the right to get the percentage increase of 16.6...%.

Since it said to round to the nearest tenth, rounding it makes the answer of 17.0% or 17% because since 6 is bigger than 10, we needed to round up and thus the answer is 17%.

2. A circular patio has a diameter of 18 feet. How
many square feet of tile will it take to cover the
patio?

Answers

Answer:  So to cover the patio it would take 255 whole tiles.  254.469 if you want to be exact.

Step-by-step explanation:

When finding flooring needed we are finding for area.  We know the formula for finding the area of a circle is A=[tex]\pi r^{2}[/tex] so we plug in our known variables...

we know r because radius is half of diameter and diameter was given in problem.  So half of 18 is 9.

r=9

A=[tex]\pi 9^{2}[/tex]

A=[tex]\pi[/tex]81

A=254.469

A social psychologist wants to assess whether there are geographical differences in how much people complain. The investigator gets a sample of 20 people who live in the Northeast and 20 people who live on the West Coast and asks them to estimate how many times they have complained in the past month. The mean estimated number of complaints from people living on the West Coast was 9.5, with a standard deviation of 2.8. The mean estimated number of complaints that people in the Northeast reported making was 15.5, with a standard deviation of 3.8. What can the researcher conclude? Use alpha of .05.

Answers

The researcher can conclude that there is a statistically significant difference in the mean number of complaints between people living on the West Coast and those living in the Northeast.

To determine if there are geographical differences in how much people complain between the Northeast and the West Coast, we can conduct a hypothesis test.

Null hypothesis (H0): There is no difference in the mean number of complaints between the Northeast and the West Coast.

Alternative hypothesis (H1): There is a difference in the mean number of complaints between the Northeast and the West Coast.

Given the sample statistics, we can perform a two-sample independent t-test to compare the means of the two groups.

Let's calculate the test statistic and compare it to the critical value at a significance level of α = 0.05.

The West Coast sample has a mean (x1) of 9.5 and a standard deviation (s1) of 2.8, with a sample size (n1) of 20.

The Northeast sample has a mean (x2) of 15.5 and a standard deviation (s2) of 3.8, with a sample size (n2) of 20.

Using the formula for the pooled standard deviation (sp), we can calculate the test statistic (t):

sp = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

t = (x1 - x2) / (sp * sqrt(1/n1 + 1/n2))

Calculating the test statistic:

sp = sqrt(((19 * 2.8^2) + (19 * 3.8^2)) / (20 + 20 - 2)) ≈ 3.273

t = (9.5 - 15.5) / (3.273 * sqrt(1/20 + 1/20)) ≈ -4.63

Using a t-table or a statistical calculator, we can find the critical value for a two-tailed t-test with α = 0.05 and degrees of freedom (df) = n1 + n2 - 2 = 38. The critical value is approximately ±2.024.

Since the absolute value of the test statistic (4.63) is greater than the critical value (2.024), we reject the null hypothesis.

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Experimental Probability is ___________ .
a . our prediction
b. data from our experiment

Answers

Answer:

its B

Step-by-step explanation:

Answer:

b. data from our experiment

Step-by-step explanation:

Choose the equation and the slope of the line that passes through (5, -3) and is perpendicular to the x-axis. A. Equation: x= -3 B. Slope: undefined C. Slope: 0 D. Equation: y = -3 E. Equation: x = 5 E Equation: y = 5​

Answers

Y=64.1x
I know this because I just did it on a piece of paper

HELP ASAP PLEASE ILL MARK BRAINLIEST AND RATE 5 STARS PLEASEEE
A survey about the student government program at a school finds the following results:
190 students like the program
135 students think the program is unnecessary
220 students plan on running for student government next year.

If a circle graph were made from this data, what would the measure of the central angle be for the group that likes the program? Round your answer to the nearest whole number. Make Sure To Show Your Steps

Answers

Answer: 126 degrees

there are 360 degrees in a circle.  

The speed of light is 3 × 108 meters per second. It take 1.82 × 102 seconds for light to reach Mars. What is the distance, in meters, between the sun and Mars? A 4.82 x 1016 B 4.82 x 1010 C 5.46 x 1016 D 5.46 x 1010

Answers

Answer:

D 5.46 x 10^10

Step-by-step explanation:

Recall that  speed is the rate of change of distance with time and may be expressed mathematically as

speed = Distance/time

Distance = speed * time

Hence given that the speed of light

= 3 × 10^8 meters per second

Time taken for light to travel between the given distance

= 1.82 × 10^2 seconds

substituting the given values

Distance = 3 × 10^8 * 1.82 × 10^2

= 5.46 * 10^(8+2)

= 5.46 * 10^10 meters

"Let C be a semialgebra on a set X. Let A = {0} U {U}=1 A; : n E N, {A1, ... , An} C C, disjoint}. = : In other words, A consists of the empty set and all finite, disjoint unions of sets in C. Prove that A is an algebra on X.
"

Answers

The set A, defined as A = {∅} ∪ {⋃_{i=1}^n Ai : n ∈ ℕ, {Ai} ⊆ C, disjoint}, is proven to be an algebra on a set X.

To prove that A is an algebra, we need to show that it satisfies three conditions: (1) X ∈ A, (2) for any set A ∈ A, its complement X\A also belongs to A, and (3) for any sets A, B ∈ A, their union A ∪ B also belongs to A.

First, the empty set ∅ is included in A by definition. Second, let A be any set in A, represented as A = ⋃_{i=1}^n Ai, where {Ai} is a collection of disjoint sets from C. Then, the complement of A is X\A, which can be represented as X\A = ⋃_{i=1}^n (X\Ai). Since each Ai is in C, their complements X\Ai are also in C, implying X\A is a disjoint union of sets from C and therefore belongs to A.

Lastly, let A and B be two sets in A, represented as A = ⋃_{i=1}^n Ai and B = ⋃_{j=1}^m Bj. The union of A and B is A ∪ B = ⋃_{i=1}^n Ai ∪ ⋃_{j=1}^m Bj. Since Ai and Bj are disjoint sets from C, their union Ai ∪ Bj is also in C. Thus, A ∪ B is a disjoint union of sets from C and belongs to A.

By satisfying all three conditions, A is proven to be an algebra on X.

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(Please help im desperate)

3. What is the perimeter of the figure graphed below?


Answers

10.6 is the correct answer

True or False The sample variance may not be always greater than the sample standard deviation

Answers

This statement is false because the sample variance is always greater than or equal to the sample standard deviation.

Variance and standard deviation are both measures of variability or dispersion within a dataset. The sample variance is defined as the average of the squared differences between each data point and the mean of the dataset. On the other hand, the sample standard deviation is the square root of the variance.

Since variance involves squaring the differences, it accounts for the spread of the dataset more effectively than the standard deviation. As a result, the sample variance tends to be larger than or equal to the sample standard deviation.

Mathematically, this relationship can be expressed as follows:

Sample Variance = [tex]\[\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}\][/tex]

Sample Standard Deviation = [tex]\[\sqrt{\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}}\][/tex]

Where x represents each data point, [tex]\(\overline{x}\)[/tex] represents the mean, and n is the sample size.

Therefore, it is not possible for the sample variance to be smaller than the sample standard deviation.

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Solve for .

Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

43 +4 < 92 +8

Answers

Answer:

[tex]x > -\frac{24}{19}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{3}x + 4 < \frac{9}{2}x + 8[/tex]

Required

Solve for x

Collect like terms

[tex]\frac{4}{3}x - \frac{9}{2}x < 8-4[/tex]

[tex]\frac{4}{3}x - \frac{9}{2}x < 4[/tex]

Take LCM

[tex]\frac{8x - 27x}{6} < 4[/tex]

[tex]\frac{-19x}{6} < 4[/tex]

Multiply by 6

[tex]6 * \frac{-19x}{6} < 4 * 6[/tex]

[tex]-19x < 24[/tex]

Divide by -19

[tex]x > -\frac{24}{19}[/tex]

sooooooooo
technically i've neevr lost a fight with a tiger

Answers

Answer:

oh thats cool

Step-by-step explanation:

 

The shaded sector above covers 1/3 of the circle. If the radius of the circle above is 3 cm, what is the area of the sector in terms of ?

Answers

Given:

The shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.

Radius of the circle = 3 cm

To find:

The area of the sector in terms of π.

Solution:

The area of a circle is

[tex]A=\pi r^2[/tex]

Substituting [tex]r=3[/tex], we get

[tex]A=\pi (3)^2[/tex]

[tex]A=9\pi[/tex]

It is given that the shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.

The area of shaded sector [tex]=\dfrac{1}{3}A[/tex]

                                             [tex]=\dfrac{1}{3}(9\pi)[/tex]

                                             [tex]=3\pi[/tex]

Therefore, the area of shaded sector is 3π sq. cm.

-48+6
+(-3)(-4) (-2)
-7​

Answers

Answer:

-73

Step-by-step explanation:

-48+6-24-7 = -73

here you gooooooooooooooooo

True/False Questions: For statements that are true, give a very short expla- nation. For statements that are false, give an example. (a) If A is an invertible matrix, then A is an invertible matrix. (b) If A is an invertible matrix, then A+ A is an invertible matrix. (c) If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. (d) If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix.

Answers

(a) If A is an invertible matrix, then A is an invertible matrix. - True

Explanation:

If A is invertible, then A has an inverse matrix A^(-1).

(b) If A is an invertible matrix, then A+ A is an invertible matrix. - False

Explanation:

A+ A = 2A is invertible if and only if A is invertible.

Therefore, this statement is false.

(c)

If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. - False

Explanation:

Even if AB is invertible, it is not always true that B is invertible.

For instance, if A = [1 0], B = [0 1],

then AB = [0 1] which is invertible, but B is not invertible.

(d)

If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix. - False

Explanation:

If A = [2 0], B = [0 1], then both A and B are invertible, but A - B = [2 -1] is not invertible.

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Find the area of the shaded sector below.

Answers

Answer:

9.07571212

Step-by-step explanation:

To solve this we first need to find the area of the circle, r squared times pi

4 x 4 x pi = 50.2654825

Now we multiply this by 65/360, 50.2654825 x 65/360 = 9.07571212

The shaded sector covers 9.07571212 square inches.

(っ◔◡◔)っ ♥ Hope It Helps & Please Consider Giving Brainliest♥

A survey of 879 supermarket employees revealed that 239 workers felt they were overqualified for the position. What is the best way to characterize the 879 employees?

Answers

Answer:

they doubt if they're qualified or not

2. kiran is flying a kite. he gets tired, so he stakes the kite into the ground. the kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. how high is the kite?

a. 9√3 feet
b. 9 feet
c. 18/√2 feet
d. 18/√3 feet

Answers

If kite is on a string that is 18 feet long, then the height of kite is (b) 9 feet.

In order to find the height of the kite, we use trigonometry. We know that the length of the string is 18 feet and the angle with the ground is 30 degrees, we use the Sine function to determine the height of the kite.

The formula to find the height is:

Height = (Length of string) × Sin(Angle),

Substituting the values,

We get,

Height = (18 feet) × Sin(30 degrees),

Using the value of Sine of 30 degrees as (0.5), we can calculate the height as :

Height = (18 feet) × (0.5),

= 9 feet

Therefore, the correct option is (b) 9 feet.

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which of the following segments is a diameter of 0?​

Answers

Answer:

ZX

Step-by-step explanation:

Please help me find the value of x for this trig question

Answers

Answer:

11.330

Step-by-step explanation:

Answer:

x=11.3

Step-by-step explanation:

Hello There!

We can use trigonometry to solve for x

Remember these are the trigonometric ratios

SOHCAHTOA

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

We can use the angle that has a measure of 31 degrees

We are given the hypotenuse and we need to find its opposite side

hypotenuse and opposite corresponds with sine so we will use sine to create an equation

(remember sin = opposite over hypotenuse)

[tex]sin(31)=\frac{x}{22}[/tex]

now that we have created an equation we solve for x

step 1 multiply each side by 22

[tex]sin(31)*22=22sin(31)\\\frac{x}{22} *22=x\\x=22sin(31)\\sin(31)=0.5150380749\\0.5150380749*22=11.33083765\\x =11.33083765[/tex]

finally we round to the nearest tenth and get that x = 11.3

Erin has 5/4 quarts of paint and she needs 2/8 of paint for each stair-step and how much paint can Erin exactly paint

Answers

Answer:

5 steps

Step-by-step explanation:

Turn 5/4s into 10/8s and it becomes really easy

The number of steps Erin could paint if he has 5/4 parts of paint, and she needs 2/8 of paint for each stair step, is 5.

What is division?

It is a basic operation of mathematics in which you divide a number into smaller parts.

Given:

Erin has 5/4 quarts of paint,

2/8 of paint for each stair-step,

Calculate the number of steps painted as shown below,

Number of steps = total paint / paint required for each step

Number of steps = 5/4 / 2/8

Number of steps =

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How to multiply fractions

Answers

Answer:

Answer Below:

Step-by-step explanation:

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.

Examine the number pattern below. 1,203, 1,624, 2,045, 2,466 ... What rule does this pattern follow? Write the next three numbers in the pattern. If the pattem continues, what will the 10 number in the sequence be? Examine the number pattern below. 10,000, 9,899, 9,798, 9,697 ... What rule does this pattern folow? Write the next three numbers in the pattern if the patter continues, what will the 11" number in the sequence be? 3. Examine the number pattern below. 5,554, 5,274, 4,994, 4.714 ... What rule does this pattern follow? Write the next three numbers in the pattern. It the patter continues, what will the 12 number in the sequence be?

Answers

1. Next three numbers: 2,887, 3,308, 3,729. Tenth number: 5,905.

2. Next three numbers: 9,596, 9,495, 9,394. Eleventh number: 9,293.

3. Next three numbers: 4.434, 4.154, 3.874. Twelfth number: 3.594.

How to continue these number patterns?

Let's examine each number pattern one by one:

1. Pattern: 1,203, 1,624, 2,045, 2,466 ...

  Rule: Each number in the pattern is obtained by adding 421 to the previous number.

  Next three numbers: 2,887, 3,308, 3,729

  Tenth number: 5,905

2. Pattern: 10,000, 9,899, 9,798, 9,697 ...

  Rule: Each number in the pattern is obtained by subtracting 101 from the previous number.

  Next three numbers: 9,596, 9,495, 9,394

  Eleventh number: 9,293

3. Pattern: 5,554, 5,274, 4,994, 4.714 ...

  Rule: Each number in the pattern is obtained by subtracting 280 from the previous number.

  Next three numbers: 4.434, 4.154, 3.874

  Twelfth number: 3.594

Therefore, based on the given patterns, the next three numbers and the specified numbers in the sequences would be as follows:

1. Pattern: 2,887, 3,308, 3,729 ... 5,905 (10th number)

2. Pattern: 9,596, 9,495, 9,394 ... 9,293 (11th number)

3. Pattern: 4.434, 4.154, 3.874 ... 3.594 (12th number)

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Which expression is equivalent to 4n(6n + 2m)?
A 24n + 4n + 2m
B (4n + 2m) x 6n
C 24n2 + 8mn
D 10n2 + 6mn

Answers

Answer:

c maybe

Step-by-step explanation:

4n(6n+2m)

24n²+8mn

Answer: C, 24n²+8mn

Step-by-step explanation:

So because 4n is on the outside of the bracket, you have to times everything on the inside of the bracket by 4n.

So, you do:

4n×6n=24n² (4×6=24 and n×n=n²)

4n×2m=8mn (4×2=8 and n×m=mn)

Then you add 24n² to 8mn like this:

24n²+8mn

Hope this helps :)

Find the value of x. Round to the
nearest tenth.
12
Х
2597
X = ?
Enter

Answers

Answer:

x ≈ 5.1

Step-by-step explanation:

Using the sine ratio in the right triangle

sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{12}[/tex] ( multiply both sides by 12 )

12 × sin25° = x , that is

x≈ 5.1 ( to the nearest tenth )

Help me with the please

Answers

Answer:

32 degrees.

Step-by-step explanation:

Plz help is it the same?

Answers

Answer:

12.054 < 12.54

Step-by-step explanation:

12.054 is less than 12.54 because it has a zero in the tenths place, and 12.54 has a five in the tenths place! Always check the first spot after the decimal first. Best of luck<3

Answer:

12.054 < 12.54

Step-by-step explanation:

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