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mamaluj [8]
3 years ago
13

Your local school board wants to determine the proportion of people who plan on voting for the school levy in the upcoming elect

ion. They conduct a random phone poll, where they contact 150 individuals and ask them whether or not they plan on voting for the levy. Of these 150 respondents, 78 people say they plan on voting for the levy. The school board wants to determine whether or not the data supports the idea that more than 50% of people plan on voting for the levy. Calculate the p-value for the one-sided Hypothesis test described in this example. (Hint: Find the test statistic and then use the tables to find the p-value.)
Mathematics
1 answer:
monitta3 years ago
5 0

Answer:

The p-value for the one-sided Hypothesis test described in this example is 0.3121.

Step-by-step explanation:

Test the hypothesis that more than 50% of people plan on voting for the levy.

At the null hypothesis, we test that the proportion is 50%, that is:

H_0: p = 0.5

At the alternate hypothesis, we test if this proportion is above 50%, that is:

H_a: p > 0.5

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that \mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5

Of these 150 respondents, 78 people say they plan on voting for the levy.

This means that n = 150, X = \frac{78}{150} = 0.52

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.52 - 0.5}{\frac{0.5}{\sqrt{150}}}

z = 0.49

Pvalue of the test:

The pvalue of the test is the probability of finding a proportion above 0.52, which is 1 subtracted by the pvalue of z = 0.49.

Looking at the z-table, z = 0.49 has a pvalue of 0.6879.

1 - 0.6879 = 0.3121

The p-value for the one-sided Hypothesis test described in this example is 0.3121.

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A sailboat leaves port and sails 12 kilometers west and then 9 kilometers north.
GarryVolchara [31]

Answer:  The sailboat is at a distance of 15 km from the port.

Step-by-step explanation:  Given that a sail boat leaves port and sails 12 kilometers west and then 9 kilometers north.

We are to find the distance between the sailboat from the port in kilometers.

Since the directions west and north are at right-angles, we can visualize the movement of the sailboat in the form of a right-angled triangle as shown in the attached figure.

The sailboat moves leaves the port at P and reach O after sailing 12 km west. From point O, again it moves towards north 9 km and reach the point S.

PS = ?

Using the Pythagoras theorem, we have from right-angled triangle SOP,

Thus, the sailboat is at a distance of 15 km from the port.

3 0
3 years ago
6. In right triangle ABC, mZC=3y-10,
lorasvet [3.4K]

Answer:

scalene

Step-by-step explanation:

step 1

Find the value of y

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

In this problem

m∠A+m∠B+m∠C=180°

substitute the given values

90\°+(y+40)\°+(3y-10)\°=180\°

Solve for y

4y+120=180

4y=180-120

4y=60

y=15

step 2

<em>Find the measure of angle B</em>

m∠B=(y+40)°

substitute the value of y

m∠B=(15+40)=55°

step 3

<em>Find the measure of angle C</em>

m∠C=(3y-10)°

substitute the value of y

m∠C=(3(15)-10)=35°

The three interior angles are different

so

The three sides of the ABC triangle will also be different

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The right triangle ABC is scalene

6 0
2 years ago
HELP PLEASE <br> solve the right triangle
aleksandrvk [35]

Answer:

Part 1) FG=4.4\ units

Part 2) EF=3.9\ units

Part 3) m\angle G=63^o

Step-by-step explanation:

step 1

Find the measure of length side FG

In the right triangle EFG

we know that

sin(27^o)=\frac{GE}{FG} ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

sin(27^o)=\frac{2}{FG}

FG=\frac{2}{sin(27^o)}=4.4\ units

step 2

Find the measure of length side EF

In the right triangle EFG

we know that

cos(27^o)=\frac{EF}{FG} ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

cos(27^o)=\frac{EF}{4.4}

EF=cos(27^o)(4.4)=3.9\ units

step 3

Find the measure of angle G

we know that

m\angle G+27^o=90^o ---> by complementary angles in a right triangle

m\angle G=90^o-27^o=63^o

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the answer is d. my shlime

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