State the hypotheses. Describe a Type I and Type II error in the context of the...

State the hypotheses. Describe a Type I and Type II error in the context of the problem and a consequence of each. Determine which type is most serious. State whether alpha should be set high or low (based on whether or not you feel a Type I error is the most serious or not).

The state of Georgia is considering spending $350 million on a computerized mathematics curriculum that for grades 3 – 10. They pilot the program with 250 students in grades 5 and 6 whose end-of-course test scores are compared to the state average score of 150.

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Expert Solution

Null Hypothesis(H0): μ = 150 Test scores will be equal to 150

Alternate Hypothesis(Ha ): μ > 150 Test scores will not be equal to 150

	The null hypothesis is True	The null hypothesis is False
We rejected Null Hypothesis	Type 1 error(alpha) Rejecting a true null hypothesis	CORRECT DECISION
We failed to reject Null Hypothesis	CORRECT DECISION	Type 2 error(beta) failing to reject a false null hypothesis

	The null hypothesis is True (H0): μ = 150	The null hypothesis is False (Ha ): μ > 150
Program is effective	Type 1: The test scores remain at 150 but the program is judged to be effective	CORRECT DECISION
Program is ineffective	CORRECT DECISION	Type 2: The test scores improve but the program is judged to be ineffective

So, Type 1 error will be when computerized mathematics doesn't performs better, but we got results which says it gives better results. Thereby, Falsely claiming that computerized math works better Implication: State spends needless $350 million

So, Type 1 error will be when computerized mathematics performs better, but we got results which says it doesn't gives better results. Type II: Falsely claim no difference between new and old (and spend no money) Implication: No money spent, computer company (likely) tries to improve product and retest.

Type 1 error is the most serious one, because lot of money will be spent on computerized mathematics curriculum.And if we falsely claim it to be working better, but actually it is not. Then all the money which is spent is a waste.

Alpha should be set low to minimize the Type 1 error. because by minimizing alpha, we are minimizing the probability of type 1 error.

orchestra answered 1 year ago

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