3.3002x10^23 how can you solve this?

Let n1equals50, Upper X 1equals30, n2equals50, and Upper X 2equals10. Complete parts (a) and (b) below. a. At the 0.05 leve

Viefleur [7K]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082$

$p_v =2*P(Z>4.082)=4.46x10^{-5}$

So the p value is a very low value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.

Step-by-step explanation:

1) Data given and notation

$X_{1}=30$ represent the number of people with a characteristic in 1

$X_{2}=10$ represent the number of people with a characteristic in 2

$n_{1}=50$ sample of 1 selected

$n_{2}=50$ sample of 2 selected

$p_{1}=\frac{30}{50}=0.6$ represent the proportion of people with a characteristic in 1

$p_{2}=\frac{10}{50}=0.2$ represent the proportion of people with a characteristic in 2

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion 1 is different from proportion 2 , the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{30+10}{50+50}=0.4$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082$

4) Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a two sided test the p value would be:

$p_v =2*P(Z>4.082)=4.46x10^{-5}$

So the p value is a very low value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.

3 0

2 years ago

How to solve these two problems ？

puteri [66]

8) $\theta$ is -0.896 radians

9) length of arc is 41.91 cm

Solution:

8)

Given that,

$tan\ \theta = \frac{-5}{4}$

$\theta$ is in quadrant 4

To find: $\theta$

From given,

$tan\ \theta = \frac{-5}{4}\\\\\theta = tan^{-1} \frac{-5}{4}\\\\\theta = tan^{-1} (-1.25)\\\\\theta = -51.34$

Thus value of $\theta$ is -51.34 degrees

Convert degrees to radians

$-51.34\ degree = -51.34 \times \frac{ \pi }{180}\ radian\\\\-51.34\ degree = -0.896\ radian$

Thus $\theta$ is -0.896 radians

9)

From given,

radius = 15.4 cm

$\theta = \frac{13 \pi }{15}$

<em><u>The length of arc when angle in radians is:</u></em>

$arc\ length = r \times \theta\\\\arc\ length = 15.4 \times \frac{ 13 \pi }{15}\\\\arc\ length = 15.4 \times 2.721\\\\arc\ length = 41.91$

Thus length of arc is 41.91 cm

4 0

2 years ago

Jillian walked 0.5 miles before she started jogging at an average pace of 5 miles per hour. The equation d = 0.5 + 5t can be use

viktelen [127]

For this case we have the following equation:
d = 0.5 + 5t
We will describe the equation step by step.
0.5: Initial distance Jillian walked
5: speed with which Jillian begins to jog
t: independent variable that indicates the number of hours
y: dependent variable that indicates the distance traveled in miles
Answer:
The variable variable is time and the dependent variable is distance.

3 0

2 years ago

Read 2 more answers

Suppose f(x) = x2 and g(x) = (3x)2. Which statement best compares the graph

Ksenya-84 [330]

Answer:

Step-by-step explanation:

Please use " ^ " to indicate exponentiation: f(x) = x^2 and g(x) = (3x)^2.

g(x) can be rewritten as 9x^2.

The graph of g(x) is only one ninth as wide as that of f(x).

Next time please share the possible answer choices. Thank you.

6 0

2 years ago

Find the values of a and b so that the solution of the linear system is (-9,1).

Diano4ka-milaya [45]

Answer:

Step-by-step explanation:

we can write -9 instead of x and y=1 instead of 1

so we write solution again

-9a+1b=-31

-9a-1b=-41

-18a=-72

a=4

we should write 4 instead of a

-9(4)+1b=-31

-36+b=-31

b=5

a=4

6 0

2 years ago