State the Type I and Type II errors in complete sentences given the following statements:                                                                             A. At most 60% of Americans vote in the U.S. presidential election.

    B. The mean number of cars a person owns in his oe her lifetime is not more than 10.

    C. About half of Americans perfer to live away from cities, given the choice.

    D. Europeans have a mean paid vacation each year of six weeks.

    E. The chance of developing breast cancer is under 11% for woman.
asked May 14 in Statistics Answers by anonymous

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1 Answer

                                                                   

    A₀. At most 60% of Americans vote in the U.S. presidential election.

    A₁. More than 60% of Americans vote in the U.S. presidential election.

    B₀. The mean number of cars a person owns in his or her lifetime is not more than 10.

    B₁. The mean number of cars a person owns in his or her lifetime is more than 10.

    C₀. About half of Americans prefer to live away from cities, given the choice.

    C₁. There is an uneven balance of Americans preferring to live near to or away from cities, given the choice.

    D₀. Europeans have a mean paid vacation each year of six weeks.

    D₁. The mean number of weeks Europeans have as paid vacation is different from six.

    E₀. The chance of developing breast cancer is under 11% for women.

    E₁. The chance of developing breast cancer is at least 11% for women.

 

 

STATEMENT

 

 

 

TRUE

FALSE

DECISION 

TRUE (accept)

OK

TYPE II

 

FALSE (reject)

TYPE I

OK

The given statements have been presented in pairs. The statement subscripted zero is H₀, the null hypothesis, the actual given statement, while the statement subscripted 1 is H₁, the alternate hypothesis, an opposite statement.

Type I errors are shown in the true-false table. Type I means rejecting H₀ when it turns out to be true; Type II means failing to reject (i.e., accepting) H₀ when it turns out to be false. For example, if A₀ is in fact true then affirming (deciding) A₁ is a Type I Error. But if A₀ is in fact false, then affirming (deciding) and accepting A₀ is a Type II Error. Decisions are made by testing the hypotheses statistically.

By applying the table to the given pairs of statements you can determine what constitutes the two types of error.

answered May 15 by Rod Top Rated User (559,640 points)

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