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Allushta [10]
4 years ago
15

Verify that( a+b)+c=a+(b+c) where a=-1/2 b=3/4 c=5/7​

Mathematics
1 answer:
mojhsa [17]4 years ago
6 0

Step-by-step explanation:

(a + b) + c \\  =   \bigg(-  \frac{1}{2}  +  \frac{3}{4} \bigg ) +  \frac{5}{7}  \\ =   \bigg(-  \frac{2}{4}  +  \frac{3}{4} \bigg ) +  \frac{5}{7}  \\  =    \frac{1}{4} +  \frac{5}{7}  \\   =  \frac{7 + 20}{28}  \\    \red{ \bold{\therefore \: (a + b) + c=  \frac{28}{28}}}...(1) \\  \\ a + (b + c) \\  =  -  \frac{1}{2}  +  \bigg( \frac{3}{4}  +  \frac{5}{7}  \bigg) \\ =  -  \frac{1}{2}  +  \bigg( \frac{21 + 20}{28}   \bigg) \\ =  -  \frac{1}{2}  +   \frac{41}{28}   \\  =  \frac{ - 14 + 41}{28}  \\  \red{ \bold{a + (b + c)  =  \frac{ 27}{28}}}....(2)  \\  \\ from \: equations \: (1) \: and \: (2) \: it \: is \\ obvious \: that:  \\  \:  \:  \: \purple{  \boxed{\bold{ (a + b )+ c = a + (b + c)  }}} \\   \:  \:  \: hence \: verified.

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Answer:

Correct option: Type II error.

Step-by-step explanation:

In statistical hypothesis testing two kind of errors can be committed by the researcher.

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The power of the test is defined as the probability of rejecting a false null hypothesis. It is denoted by <em>β</em>.

Then the probability of Type II error can be defined as:

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The power of the test is affected by the significance level<em>.</em>

If the significance level is less than the power is also less.

The significance level is related to the <em>p</em>-value of the test.

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