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4 years ago

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All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make

a statistical inference about the mean of the normally distributed population from which it was drawn? . The margin of error is multiplied by . The margin of error is multiplied by . The margin of error is multiplied by 0.5. The margin of error is multiplied by 2.

1 answer:

gizmo_the_mogwai [7]4 years ago

8 0

Answer:

The margin of error is multiplied by $\sqrt{2}$

Step-by-step explanation:

margin of error (ME) from the mean can be calculated using the formula

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic of the given confidence level

s is the standard deviation of the sample (or of the population if it is known)

N is the sample size

Since margin of error is proportional with inverse of $\sqrt{N}$ ,

if we cut the sample size in half, the margin of error is multiplied by $\sqrt{2}$ .

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Sindrei [870]

2.1%

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4 years ago

The R. R. Bowker Company collects information on the retail prices of books and publishes the data in The Bowker Annual Library

Alina [70]

Answer:

a) $t=\frac{54.97-57.61}{\frac{8.45}{\sqrt{28}}}=-1.653$

The degrees of freedom are given by:

$df=n-1=28-1=27$

$p_v =2*P(t_{(27)}$

b) The conclusion depends on the significance level selected, if the p value is lower than a significance level given we have enough evidence to conclude that the true mean is different from 57.61, otherwise we FAIl to reject the null hypothesis and thare is no evidence to conclude that the true mean is different from 57.61

Step-by-step explanation:

Data provided

$\bar X=54.97$ represent the mean for the retail price

$s=8.45$ represent the sample standard deviation

$n=28$ sample size selected

$\mu_o =57.61$ represent the value that we want to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value for the test

Part a

System of hypothesis

We want to check if the true mean for the reatil price is 57.61 or not, the system of hypothesis would be:

Null hypothesis: $\mu = 57.61$

Alternative hypothesis: $\mu \neq 57.61$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic is given by:

$t=\frac{54.97-57.61}{\frac{8.45}{\sqrt{28}}}=-1.653$

P value

The degrees of freedom are given by:

$df=n-1=28-1=27$

The p value would be:

$p_v =2*P(t_{(27)}$

Part b: Conclusion

The conclusion depends on the significance level selected, if the p value is lower than a significance level given we have enough evidence to conclude that the true mean is different from 57.61, otherwise we FAIl to reject the null hypothesis and thare is no evidence to conclude that the true mean is different from 57.61

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3 years ago

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faltersainse [42]

Answer:

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Step-by-step explanation:

Given

1 inch = 14 feet

Required

Find the equivalent of 199 feet

Write out the given expression;

1 inch = 14 feet

Let x represent the equivalent of 199 feet in inches; Such that:

x = 199 feet

Write out both expressions

1 inch = 14 feet

x = 199 feet

Using cross multiplication; both expressions become

x * 14 feet = 199 feet * 1 inch

Divide both sides by 14 feet

$\frac{x * 14 feet}{14 feet} = \frac{199 feet * 1 inch}{14 feet}$

$\frac{x * 14}{14} = \frac{199* 1 inch}{14}$

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$x = \frac{199* 1 inch}{14}$

$x = \frac{199inch}{14}$

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Answer:

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Step-by-step explanation:

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lana66690 [7]

The correct answer is K.

The answer is <span>0<x</span><<span>32</span>

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