Mathematics, 30.11.2019 05:31 madmar

The mean monthly expenditure on gasoline per household in middletown is determined by selecting a random sample of 100 households. the sample mean is $128, with a sample standard deviation of $38, what is the upper bound of a 90% confidence interval for the mean monthly expenditure on gasoline per household in middletown? a. $134.66 b. $162.20 c. $129.38 d. $131.42 e. $13287

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Answer from: hannaharsena

a. $134.66

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =128$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=38 represent the sample standard deviation

n=100 represent the sample size

2) Calculate the confidence interval

Since the sample size is large enough n>30. The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$128-1.64\frac{38}{\sqrt{100}}=121.768$

$128+1.64\frac{38}{\sqrt{100}}=134.232$

The closest value would be $134.66 and that would be the answer for this case.

Answer from: Quest

jjhjhhjjh

step-by-step explanation:

What is the best window on a graphing calculator to see the graph?

Answer from: Quest

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b): y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4 perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

Which equation represents a line perpendicular to the line shown on the graph?

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