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11111nata11111 [884]
2 years ago
5

The value of a dirt bike decreases by 20% each year. If you purchased this dirt bike today for $500, to the nearest dollar how m

uch would the bike be worth five years later?
Mathematics
1 answer:
Akimi4 [234]2 years ago
3 0
After the first year: 500*0.8
After the second year: 500*0.8^2
After the third year 500*0.8^3
After the fourth year 500*0.8^4
After the fifth year: 500*0.8^5 = 163.84

Answer: $ 164
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Step-by-step explanation:

Data given and notation

n=502 represent the random sample taken

X=331 represent the adults that said they would not be bothered if the NAtional security agency

\hat p=\frac{331}{502}=0.659 estimated proportion of people who would not be bothered if the NAtional security agency

p_o=0.5 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than the majority of 0.5:  

Null hypothesis:p\leq 0.5  

Alternative hypothesis:p > 0.5  

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.

Calculate the statistic  

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

z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124  

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The significance level provided \alpha=0.01. The next step would be calculate the p value for this test.  

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