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3 years ago

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A restaurant manager needs to rope off a rectangular section for a private party. The length of the section must be 7.4 m. The m

anager can use no more than 23 m of rope. Which inequality could you use to find the possible widths of the roped off section

1 answer:

sergij07 [2.7K]3 years ago

4 0

Answer:

$14.8+2W\leq 23$

The value of the width must be less than or equal to 4.1 meters

Step-by-step explanation:

we know that

The perimeter of the rectangular section is given by

$P=2L+2W$

we have

$L=7.4\ m$

substitute

$P=2(7.4)+2W$

$P=14.8+2W$

Remember that

The manager can use no more than 23 m of rope

so

The perimeter must be less than or equal to 23 m

$14.8+2W\leq 23$

solve for W

subtract 14.8 both sides

$2W\leq 23-14.8$

$2W\leq 8.2$

divide by 2 both sides

$W\leq 4.1\ m$

The value of the width must be less than or equal to 4.1 meters

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The number of events is 29, the number of trials is 298, the claimed population proportion is 0.10, and the significance leve

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Answer:

$z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155$

$p_v =2*P(Z$

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .

Step-by-step explanation:

1) Data given and notation

n=298 represent the random sample taken

X=29 represent the events claimed

$\hat p=\frac{29}{298}=0.0973$ estimated proportion

$p_o=0.1$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is 0.1 or no.:

Null hypothesis: $p=0.1$

Alternative hypothesis: $p \neq 0.1$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .

We can do the test also in R with the following code:

> prop.test(29,298,p=0.1,alternative = c("two.sided"),conf.level = 1-0.05,correct = FALSE)

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