In a survey, the planning value for the population proportion is p* = 0.26. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05? (Round your answer up to nearest whole number.)

n = 296

Sample size n = 296

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

x+/-M.E

M.E = z√(p(1-p)/n)

Making n the subject of formula;

n = (p(1-p)/(M.E/z)^2) 1

Given that;

Proportion p = 0.26

Number of samples n = ?

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values into equation 1;

n = (0.26(1-0.26))/((0.05/1.96)^2)

n = 295.649536

n = 296

Sample size n = 296

(2, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Distributive Property

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

2x + y = 5

3x - 2y = 4

Step 2: Rewrite Systems

Manipulate 1st equation

[Subtraction Property of Equality] Subtract 2x on both sides:                      y = 5 - 2x

Step 3: Solve for x

Substitution

Substitute in y [2nd Equation]:                                                                         3x - 2(5 - 2x) = 4[Distributive Property] Distribute -2:                                                                3x - 10 + 4x = 4[Addition] Combine like terms:                                                                        7x - 10 = 4[Addition Property of Equality] Add 10 on both sides:                                   7x = 14[Division Property of Equality] Divide 7 on both sides:                                 x = 2

Step 4: Solve for y

Substitute in x [Modified 1st Equation]:                                                           y = 5 - 2(2)Multiply:                                                                                                             y = 5 - 4Subtract:                                                                                                            y = 1