Mathematics, 21.12.2019 00:31, danielle413

Euro coin. statistics students at the akademia podlaka conducted an experiment to test the hypothesis that the one-euro coin is biased (i. e., not equally likely to land heads up or tails up). belgian-minted one-euro coins were spun on a smooth surface, and 140 out of 250 coins landed heads up. does this result support the claim that one-euro coins are biased

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answered: NickWinston261

$z=\frac{0.56 -0.5}{\sqrt{\frac{0.5(1-0.5)}{250}}}=1.897$

p_v =2*P(z1.897)=0.0578

If we compare the p value obtained and the significance level assumed $\alpha=0.05$ we see that $p_v\alpha$ 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 heads in the Euro coins is not significantly different from 0.5.

Step-by-step explanation:

1) Data given and notation

n=250 represent the random sample taken

X=140 represent the number of heads obtained

$\hat p=\frac{140}{250}=0.56$ estimated proportion of heads

p_o=0.5 is the value that we want to test

$\alpha$ represent the significance level

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 that one-Euro coins are biased, so the correct system of hypothesis are:

Null hypothesis: p=0.5

Alternative hypothesis: $p \neq 0.5$

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 .

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np_o =250*0.5=12510

n(1-p_o)=250*(1-0.5)=12510

3) Calculate the statistic

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

$z=\frac{0.56 -0.5}{\sqrt{\frac{0.5(1-0.5)}{250}}}=1.897$

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(z1.897)=0.0578

answered: Guest

they are simplified

step-by-step explanation:

answered: Guest

answer: y = -2.5x - 15

(-6,0)

step-by-step explanation: