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wel
3 years ago
15

In the American justice system, a criminal is presumed innocent until proven guilty, meaning that the prosecution must gather en

ough evidence to prove that the defendant has actually committed a crime. Suppose a defendant is on trial for robbing a bank. The jury will hear the case and decide on a verdict of guilty or not guilty at the conclusion of the trial.
a. State the null and alternative hypotheses for the defendant. Just use words to describe the hypotheses - no statistical symbols are necessary.
b. Describe how a Type I error could occur during the trial.
c. Describe how a Type II error could occur during the trial.
d. Describe the two ways the correct decision could be made in the trial.
Mathematics
1 answer:
anastassius [24]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that in the American justice system, a criminal is presumed innocent until proven guilty, meaning that the prosecution must gather enough evidence to prove that the defendant has actually committed a crime.

H0:  The defendent is not guilty

Ha: The defendent is guilty

(Two tailed test)

a) given above

b) Type I error here is false rejection of H0, i.e. charging defendent guilty even though actually he is not guilty

c) Type II error here is accepting that the defendent is not guilty even though he is guilty

d) Whenever type I increases type II error decreases and vice versa.

But as per ethics, an innocent person should not be punished at any cost, so care should be taken to avoid type I error which is more serious than avoiding type II error.

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In a sample of 330 randomly selected PCC students it was found that 175 of them have a car. Assume this sample comes from a popu
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Answer:

a) 0.530 - 1.96\sqrt{\frac{0.530(1-0.530)}{330}}=0.47615

0.530 + 1.96\sqrt{\frac{0.530(1-0.530)}{330}}=0.58385

And if we convert this interval into % we got (47.615%, 58.385%)

b) For this case since the lower value for the confidence interval is a value lower than 0.5 (50%) we don't have enough evidence to conclude at 10% of significance than  most students at PCC own a car

Step-by-step explanation:

We can begin calculating the best estimator for the true proportion of students at PCC who own a car:

\hat p = \frac{175}{330}=0.530

Part a

The confidence level is 95% , and the significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical values would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the true proportion is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing the info given we got:

0.530 - 1.96\sqrt{\frac{0.530(1-0.530)}{330}}=0.47615

0.530 + 1.96\sqrt{\frac{0.530(1-0.530)}{330}}=0.58385

And if we convert this interval into % we got (47.615%, 58.385%)

Part b

For this case since the lower value for the confidence interval is a value lower than 0.5 (50%) we don't have enough evidence to conclude at 10% of significance than  most students at PCC own a car

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