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3 years ago

Express the confidence interval 0.866 ± 0.037 in open interval form (i.e., (0.155,0.855)).

Mathematics

1 answer:

Nostrana [21]3 years ago

5 0

Answer: (0.829, 0.903)

Step-by-step explanation:

We know that $a\pm b=(a-b,\ a+b)$ (1)

The given confidence interval : 0.866 ± 0.037

To express the given confidence interval in open interval form , we split the given expression as :

$0.866 \pm 0.037 \\\\=(0.866-0.037,\ 0.866+0.037)\ \ \text{[By using (1)]}\\\\=(0.829,\ 0.903)$

Therefore, the confidence interval in open interval form would be (0.829, 0.903) .

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3 years ago

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

melamori03 [73]

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We conclude that the mean wedding cost is less than $30,000 as advertised.

Step-by-step explanation:

We are given the following data set:(in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{236100}{8} = 29512.5$

Sum of squares of differences = 3408750

$S.D = \sqrt{\frac{3408750}{7}} = 697.82$

Population mean, μ = $30,000

Sample mean, $\bar{x}$ = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $ 697.82

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars}$ We use one-tailed t test to perform this hypothesis.

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$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975$

Now,

$t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and reject it.

We conclude that the mean wedding cost is less than $30,000 as advertised.

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4 years ago

Find the slope of the line in the graph below

Andru [333]

Answer =-3 or -3/1

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Two points on the line are (-1,2) and (-3,-4)
X1=-1 Y1=2
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(y2-y1)/(x2-x1) = (-4-2)/(-3-(-1)) =(-6)/(-3+1)
=-6/-2 = -3

So slope =-3/1 or -3 (same thing)

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3 years ago

Express the confidence interval 0.866 ± 0.037 in open interval form (i.e., (0.155,0.855)).​

Express the confidence interval 0.866 ± 0.037 in open interval form (i.e., (0.155,0.855)).