What is the value of the 12th term in the sequence 4, 12, 36, 108, ...?

A local police chief claims that 31% of all drug-related arrests are never prosecuted. A sample of 500 arrests shows that 27% of

Elis [28]

Answer:

$z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933$

$p_v =P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.02$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.

Step-by-step explanation:

1) Data given and notation

n=500 represent the random sample taken

X represent the number of arrests that were not prosecuted.

$\hat p=0.27$ estimated proportion of arrests that were not prosecuted

$p_o=0.31$ is the value that we want to test

$\alpha=0.02$ represent the significance level

Confidence=98% or 0.98

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.31.:

Null hypothesis: $p\geq 0.31$

Alternative hypothesis: $p < 0.31$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.02$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.02$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.

3 0

2 years ago

Use the rules for multiplication by powers of 10 to calculate 3 × 100

padilas [110]

3 × 100 = 300

the easiest way to do it is just add the same amount of zero's to the number you multiplied with. for example

3 × 10000 if you would just take out the zero's
it would look like this. 3 × 1

the answer of course would be 3 then you can put the zero's back in the answer (30000)

at least that's how I understood it

3 × 100 =

3 × 1(00) =
-->

-->
(00)
3 × 1(00) = 3

3 × 100 = 300

4 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D16%20-%206%20%5Csqrt%5B3%5D343%20%2B%2018%20%5Csqrt%5B5%5D243%20-%20%20%5Csqr

VladimirAG [237]

Answer:

Step-by-step explanation:

= 2- 6*7 + 18*3 - 14

=2-42+54-14

=2 + 12- 14

= 14-14

=0

6 0