In the data set below, what is the mean absolute deviation? 1, 4, 2, 8, 4, 8
1 answer:
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The equation in slope-intercept form for this function is y = 8 x
The slope represents the unit cost
A party for 40 people would cost $320
Step-by-step explanation:
The linear equation in the form of slope-intercept is:
y = mx + b, where m is the slope of the line and b is the y-intercept
, where
and
are two points on the line
- To find b substitute x and y of the equation by the coordinates of any point on the line
A caterer charges $120 to cater a party for 15 people and $200 for
25 people.
Assume that the cost, y, is a linear function of the number of people x
We need to write an equation in slope-intercept form for this function
We need to explain that the slope represent what
We need to find how much a party for 40 people would cost
∵ The slope-intercept form of the equation is y = mx + c
∵ y is the cost and x is the number of people
∴ x = 15 and y = 120 is a point on the line
∴ x = 25 and y = 200 is another point on the line
- Now we can use them to find the slope of the line
∵
∴ m = 8
∴ y = 8 x + b
- To find b substitute x by 15 and y by 120 in the equation
∴ 120 = 8(15) + b
∴ 120 = 120 + b
- Subtract 120 from both sides
∴ b = 0
∴ y = 8 x
The equation in slope-intercept form for this function is y = 8 x
∵ The slope = change of y ÷ change of x
∴ The slope = cost ÷ number of people
∴ The slope represents the cost per person
The slope represents the unit cost
∵ There are 40 people
∴ x = 40
∵ The equation of the cost is y = 8 x
∴ y = 8 × 40
∴ y = 320
∴ The cost is $320
A party for 40 people would cost $320
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Answer:
Null hypothesis:
Alternative hypothesis:
Comparing the p value with the significance level assumed we see that
so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.
Step-by-step explanation:
Data given and notation
represent the number of people indicating that their financial security was more than fair in 2012
represent the number of people indicating that their financial security was more than fair in 2010
sample 1 selected
sample 2 selected
represent the proportion estimated of people indicating that their financial security was more than fair in 2012
represent the proportion estimated of people indicating that their financial security was more than fair in 2010
represent the pooled estimate of p
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
Part a: Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Hypothesis testing
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
Since is a two sided test the p value would be:
Comparing the p value with the significance level assumed we see that
so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.