A triangle has sides with lengths of 8 centimeters, 15 centimeters, and 17 centimeters. Is it a right triangle?

According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bother

k0ka [10]

Answer:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

$p_v =P(z>7.124)=5.24x10^{-13}$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.

Step-by-step explanation:

Data given and notation

n=502 represent the random sample taken

X=331 represent the adults that said they would not be bothered if the NAtional security agency

$\hat p=\frac{331}{502}=0.659$ estimated proportion of people who would not be bothered if the NAtional security agency

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

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than the majority of 0.5:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, 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 $p_o$ .

Calculate the statistic

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

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

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 $\alpha=0.01$ . The next step would be calculate the p value for this test.

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

$p_v =P(z>7.124)=5.24x10^{-13}$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.

4 0

3 years ago

According to the 2000 Census the population of Canton was 7,720. Holly Spring's population was 3,200. Canton's population increa

Kazeer [188]

Firstly, the rate of increase of Canton = 80/7720 = 0.010
The rate of increase of HP = 120/3200 = 0.0375
Apply the formula of compound interest==> A =A'(1+i)^n
The population will be equal when the following equality is satisfied

7720(1+0.01)^n = 3200(1+0.0375)^n

or

7720x1.01^n = 3200x1.0375^n

Divide both sides by 3200 ===>(193/80)x1.01^n=1.0375^n

8 0

3 years ago

Read 2 more answers

A shop sells newspapers for a profit of 0.5%. His sales for the month of January were $8341.50. How much of this is profit?

Doss [256]

Amount of sales of newspapers for the month of January = $8341.50
Percentage of profit for which the newspaper is sold = 0.5%
Then
Amount of profit made in the month of January = 0.5% * 8341.50 dollars
   = (0.5/100) * 8341.50 dollars
   = 4170.75/100 dollars
   = 41.707 dollars
   = 41.71 dollars
So the shop makes a profit of $41.71 in the month of January by selling newspapers worth $8341.50. I hope the procedure is perfectly clear for you to understand.

8 0

3 years ago

Simplify 3√ 2 – √ 2 .

pickupchik [31]

You will have two find the square root of the question