Simplify: xy^2(-2x)(3xy)(-4x^2y)1/8x^2y^3

The probability of choosing a correct answer = 1/5
The probability of choosing a wrong answer = 4/5

Scores received on correct answer = +3
Scores received on wrong answer = -1
Scores on blank answer = 0

The average scores, in long run will be equal to the expected value. The expected value E, in this case will be:

$E= \frac{1}{5}(+3)+ \frac{4}{5}(-1)=-0.2$

Thus, in long run, the student will score -0.2 points on average.

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4 years ago

Over the past several years, the proportion of one-person households has been increasing. The Census Bureau would like to test t

bixtya [17]

Answer:

For this case we can find the critical value with the significance level $\alpha=0.05$ and if we find in the right tail of the z distribution we got:

$z_{\alpha}= 1.64$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

Step-by-step explanation:

We have the following dataset given:

$X= 43$ represent the households consisted of one person

$n= 125$ represent the sample size

$\hat p= \frac{43}{125}= 0.344$ estimated proportion of households consisted of one person

We want to test the following hypothesis:

Null hypothesis: $p \leq 0.27$

Alternative hypothesis: $p>0.27$

And for this case we can find the critical value with the significance level $\alpha=0.05$ and if we find in the right tail of the z distribution we got: