Solve the system by substitution. -2x-10y=-2 -4y=x

There are 169 million registered voters in the us. determine an interval for the number (how many) of registered democrats in th

VashaNatasha [74]

Part A:

Given that in a sample of 400 registered voters, 204 were democrats, i.e. n = 400, $\hat{p}= \frac{204}{400} =0.51$

The 95% confidence interval for the proportion of registered democrats voters in the population is given by:

$95\%\ C.I.=\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ =0.51\pm1.96\sqrt{\frac{0.51(1-0.51)}{400}}=0.51\pm1.96\sqrt{\frac{0.2499}{400}} \\ \\ =0.51\pm1.96(0.025)=0.51\pm0.049=(0.51-0.049,\ 0.51+0.049) \\ \\ =\bold{(0.461,\ 0.559)}$

Part B:

Given that there are 169 million registered voters in the US, the interval for the number of registered democrats in the population is given by

[0.461(169,000,000), 0.559(169,000,000)] = (77,909,000, 94,471,000)

6 0

2 years ago

5x^2 +3 = -122 a. no solution b. -5 c. +‐5 d. +- 25

Finger [1]

Answer:

I put it in the calc and it got

x=5i,−5i

6 0

2 years ago

Read 2 more answers

Solve the quadratic equation 3x²+2x-4=0

vivado [14]

Auuuu.........

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4 0

2 years ago

Given: x + 2 < -5. Choose the solution set.

OLEGan [10]

Answer:

x < -7

Step-by-step explanation:

to isolate x we need to subtract 2 from both sides. -5-2 is -7, so the answer is x < -7

4 0

2 years ago

Read 2 more answers

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come f

AlladinOne [14]

Answer:

$z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43$

Now we can calculate the p value with the following probability:

$p_v =P(z>2.43)=0.0075 \approx 0.008$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

$\hat p=0.64$ estimated proportion of interest

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to verify if the true proportion is higher than 0.5:

Null hypothesis: $p =0.5$

Alternative hypothesis: $p > 0.5$

The statistic is given by:

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

Replacing the info given we got:

$z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43$

Now we can calculate the p value with the following probability:

$p_v =P(z>2.43)=0.0075 \approx 0.008$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

7 0

3 years ago