Ask question

Ask question

All categories

2 years ago

12

Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numb

ers of successes to find the pooled estimate. Round your answer to the nearest thousandth.
n1 = 677 n2 = 3377
x1 = 172 x2 = 654

1 answer:

dezoksy [38]2 years ago

3 0

Answer:

The calculated value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

<u>Step-by-step explanation</u>:

<em>Given first sample size n₁ = 677</em>

<em>First sample proportion </em>

<em> </em> $p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254$ <em></em>

Given second sample size n₂ = 3377

<em>second sample proportion </em>

<em> </em> $p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936$ <em></em>

<u><em>Null Hypothesis : H₀ :</em></u><em> p₁ = p₂.</em>

<u><em>Alternative Hypothesis : H₁</em></u><em> : p₁ ≠ p₂.</em>

Test statistic

$Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }$

where

$P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}$

P = 0.2036

Q = 1 - P = 1 - 0.2036 = 0.7964

$Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }$

Z = 3.775

<em>Critical value ∝=0.05</em>

<em>Z- value = 1.96</em>

<em>The calculated value Z = 3.775 > 1.96 at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>The Two Population proportion are not equal</em>

<em></em>

You might be interested in

An American car travels 32 miles on one gallon of gas. A European car travels 12.7 kilometers on one liter of gas. Which car get

BabaBlast [244]

32 miles is the same as 19.8839 kilometers

There are 3.78541 liters in a gallon

Now we divide the two.

19.8839 / 3.78541 ≈ 5.25

The American car gets 5.25 km per liter. So the European car is better on gas economy.

5 0

2 years ago

G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

2 years ago

A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was fo

borishaifa [10]

Answer:

a) $P(5$

And we can find this probability with this difference:

$P(-1.90$

And using the norma standard distribution or excel we got:

$P(-1.90$

b) $P(X>6) =P(Z> \frac{6-7.37}{1.25}) = P(Z>-1.096)$

And using the complement rule we got:

$P(Z>-1.096) =1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(7.37,1.25)$

Where $\mu=7.37$ and $\sigma=1.25$

We are interested on this probability

$P(5$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(5$

And we can find this probability with this difference:

$P(-1.90$

And using the norma standard distribution or excel we got:

$P(-1.90$

Part b

For this case we want this probability:

$P(X>6)$

And we can use the z score and we got:

$P(X>6) =P(Z> \frac{6-7.37}{1.25}) = P(Z>-1.096)$

And using the complement rule we got:

$P(Z>-1.096) =1-P(Z$

8 0

2 years ago

If i = StartRoot negative 1 EndRoot, what is the value of i 3? –1 i 1 –i

Annette [7]

Answer:

-i

Step-by-step explanation:

Our number is i = √-1, and we want to find i³, which is essentially just i * i * i, so:

i³ = i * i * i = √-1 * √-1 * √-1 = -1 * √-1 = -1 * i = -i

The answer is -i.

5 0

2 years ago

Read 2 more answers

five people, each working 8 hours a day, can assemble 400 toys in a five day work week. what is the average number of toys assem

vladimir1956 [14]

The question asks for the rate of toys per hour.

So we shall divide the total toys assembled by the total hours.

Its a five day week.

The number of hours allotted per day are 8.

So total allotted during the week are 8 × 5 = 40 hours.

Number of toys made during the week are 400.

Hence the number of toys assembled per hour per person

= number of toys / number of hours

= 400 / 40

= 10 toys per hour per person.

The average number of toys assembled per hour per person is 10.

8 0

2 years ago

Read 2 more answers