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Pie
3 years ago
11

(3)-2 Evaluate exponent

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
7 0

Answer:

3^{-2} = \dfrac{1}{9}

Step-by-step explanation:

Definition of negative exponent:

a^{-n} = \dfrac{1}{a^n}

In our case, a = 3 and -n = -2.

3^{-2} = \dfrac{1}{3^2}

Now we just evaluate the power in the denominator.

3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{9}

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We are given that a survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each person." has been conducted. The result is that 735 of the 2625 respondents agreed, 1812 disagreed, and 78 answered ‘‘don’t know."

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where, \hat p = sample proportion of people who disagree with the statement = \frac{1812}{2625} = 0.69

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<em>Here for constructing 99% confidence interval we have used One-sample z proportion statistics.</em>

<u>So, 99% confidence interval for the population proportion, p is ;</u>

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                   of significance are -2.58 & 2.58}  

P(-2.58 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 2.58) = 0.99

P( -2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

P( \hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

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Therefore, 99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

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