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Tatiana [17]
1 year ago
8

Can anyone please help me with this question? : A target consists of two concentric circles. The larger circle has diameter 1m.

When a complete novice fires at the target, the probability of hitting the blue circle is the same as the probability of hitting the green region. Find the diameter of the blue circle.

Mathematics
1 answer:
11111nata11111 [884]1 year ago
5 0
We know that
if  <span>the probability of hitting the blue circle is the same as the probability of hitting the green region
then 
the area of the blue circle is equal to the area of the green region

Let
x----> diameter of the blue circle

area of the blue circle=pi*(x/2)</span>²----> (pi/4)*x² m²-----> equation 1

area of the green region=area of the larger circle-area of the blue circle
area of the green region=pi*(1/2)²-(pi/4)*x²
=(pi/4)-(pi/4)*x² m²----> equation 2

equate equation 1 and equation 2
(pi/4)*x²=(pi/4)-(pi/4)*x² -----> divide by (pi/4)---> x²=1-x²
2x²=1-----> x²=1/2----> x=1/√2-----> x=√2/2 m

the diameter of the blue circle is √2/2 m


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Answer:

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b) Since is a left tailed test the p value would be:  

p_v =P(Z  

c) If we compare the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.  

We can use as smallest significance level 0.044 and we got the same conclusion.  

Step-by-step explanation:

Data given and notation  

n=60 represent the random sample taken

X represent the business owners plan to provide a holiday gift to their employees

\hat p=0.35 estimated proportion of business owners plan to provide a holiday gift to their employees

p_o=0.46 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)  

Part a

On this case w ejust need to multiply the value of th sample size by the proportion given like this:

Number = 60 *0.35=21

2) Part b

We need to conduct a hypothesis in order to test the claim that the proportion of business owners providing holiday gifts had decreased from the 2008 level:  

Null hypothesis:p\geq 0.46  

Alternative hypothesis:p < 0.46  

When we conduct a proportion test we need to use the z statisitc, 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.

Calculate the statistic  

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

z=\frac{0.35 -0.46}{\sqrt{\frac{0.46(1-0.46)}{60}}}=-1.710  

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 significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(Z  

Part c

If we compare the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.  

We can use as smallest significance level 0.044 and we got the same conclusion.  

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