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Answer:
Being p1 the proportion for people of ages 36-50 and p2 the proportion for people of ages 21-35, the null and alternative hypothesis will be:
Step-by-step explanation:
A hypothesis test on the difference of proportions needs to be performed for this case.
We have two sample proportions and we want to test if the true population proportions differ from each other, usign the information given by the sample statistics.
The claim is that the proportion of people of ages 36-50 who own homes is significantly greater than the proportin of people age 21-35 who own homes.
The term "higher" will define the alternative hypothesis, that is the hypothesis that represents what is claimed. The null hypothesis always include the equal sign, and will state that both proportions do not differ.
Being p1 the proportion for people of ages 36-50 and p2 the proportion for people of ages 21-35, the null and alternative hypothesis will be:
Answer:
Rate of change: m = -2/3
Value of the function at x = 24: y = 22
Step-by-step explanation:
You can write linear functions in <u>slope-intercept form</u>: y = mx + b
"x" and "y" are points on the line
"m" is the slope, how steep the line is, also known as <u>rate of change</u>
"b" is the y-intercept, when the graph hits the y-axis
Find the rate of change of the function by finding the slope between the two given points.
The formula for slope:
Label point 1 and point 2. Label each coordinate; remembered ordered pairs are (x, y).
Point 1 (6, 34) x₁= 6 y₁ = 34
Point 2 (18, 26) x₂ = 18 y₂ = 26
Substitute the points into your equation using the bolded information.
Subtract
Reduce the fraction. Top and bottom divide by 4
Slope of the line, "m"
Substitute the slope and any point you want into slope-intercept form. I choose point (6, 34). x = 6 y = 34 m = -2/3
y = mx + b
34 = (-2/3)(6) + b Multiply to simplify
34 = (-12/3) + b
Start isolating "b"
34 + 12/3 = (-12/3) + 12/3 + b Add 12/3 on both sides
34 + 12/3 = b
Add fractions by combining the whole number into the numerator. Multiply the whole number by the denominator and add to the numerator.
b = (34*3 + 12) / 3 Solve numerator
b = 114/3 Value of "b"
Substitute the values "m" and "b" into slope-intercept form.
y = -2/3 x + 114/3 Equation of the line
To find the x = 24, take the equation of the line and substitute "x" for 24. Then solve for "y".
y = -2/3 x + 114/3 Equation of the line
y = (-2/3)(24) + 114/3
y = (-2*24)/3 + 114/3 Multiply into the numerator
y = (-48)/3 + 114/3 Combine under the same denominator
y = (-48 + 114) / 3 Add
y = 66/3 Divide
y = 22 Value of function
Therefore the rate of change, or slope "m", is -2/3. When "x" is 24, the value of the entire function is 22.