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Licemer1 [7]
3 years ago
11

a study done by researchers at a university concluded that 70% of all student athletes in this country have been subjected to so

me form of hazing. The study is based on responses from 1200 athletes. What are the margin of error and 95% confidence interval for the study?
Mathematics
1 answer:
natima [27]3 years ago
6 0

Answer:The margin of error is 0.01323 and 95% confidence interval is (0.674,0.73).

Step-by-step explanation:

Since we have given that

p = 0.70

n = 1200

We need to find the margin of error;

Margin of error would be

\sqrt{\dfrac{p(1-p)}{n}}\\\\=\sqrt{\dfrac{0.7\times 0.3}{1200}}\\\\=0.01323

At 95% confidence level, α = 1.96

so, 95% confidence interval would be

p\pm z\times 0.01323\\\\=0.7\pm 1.96\times 0.01323\\\\=0.7\pm 0.02593\\\\=(0.7-0.02593,0.7+0.02593)\\\\=(0.674,0.73)

Hence, the margin of error is 0.01323 and 95% confidence interval is (0.674,0.73).

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Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8
morpeh [17]

Answer:

Step-by-step explanation:

H₀ : The distribution of the sample agrees with the population distribution.

H₁ : the distribution of the does not agree with the population distribution.

Using the  Chi-square test statistics

we will compute the expected frequencies

Now expected frequency for Washington will be

Fe = Npi = 1000×51% = 5100

expected frequency for Oregon

Fe = Npi = 1000×30% = 300

expected frequency for Idaho

Fe = Npi = 1000×11% = 110

expected frequency for  Montana

Fe = Npi = 1000×8% = 80

The Chi=square test statistics is;

x² = ∑ [ (Fo - Fe)² / Fe )

now we substitute

Given our Fo ( 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana) from the question

x² =  (450-510)²/510 + (340-300)²/300 + (150-110)²/110 + (60-80)²/80

x²= 31.9376

so the chi-square test statistics is 31.9376

Now the chi-square critical value

first we compute for degree of freedom

d.f = k -1 = 4 - 1 = 3

So from the critical value table, degree of freedom 3 and significance level 0.05,

the chi-square critical value is 7.8147

Therefore chi-square test statistics 31.9376 is greater than the chi-square critical value 7.8147, so NULL HYPOTHESIS IS REJECTED at 5% significance.

There is sufficient evidence to warrant rejection  of the claim that the distribution of the sample agrees with the distribution of the state populations.

3 0
3 years ago
Show that if u+v and u-v are orthognal, then the vectors u and v must have the same length.
pashok25 [27]

Answer with Step-by-step explanation:

We are given that

u+ v and u-v are orthogonal

We have to prove that u and v must have the same length.

When two vector a and b are orthogonal then

a\cdot b=0

By using the property

(u+v)\cdot (u-v)=0

We know that

(a+b)\cdot (a-b)=\mid a\mid^2-\mid b\mid^2

\mid u\mid ^2-\mid v\mid^2=0

\mid u\mid^2=\mid v\mid^2

Magnitude is always positive

When power of base on both sides are equal then base will be equal

Therefore,

\mid u\mid=\mid v\mid

Hence, the length of vectors u and v must have the same length.

5 0
3 years ago
I hit 20 subs! Can you guys help me out more by subbing to 999 splxsh on yt. Thanks!
charle [14.2K]

Answer:

Sure! I'll look you up!

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
The Dallas Development Corporation is considering the purchase of an apartment project for $100,000. They estimate that they wil
katovenus [111]

Answer:

  • <u>The rate of return is 8.15%</u>
  • <u>This is a good investment</u>

<u></u>

Explanation:

For the first question, you need to find the rate that makes the present value of a stream of ten constant annual payments of $15,000 equal to the $100,000 investment.

The formula that returns the present value of a constant payment is called the annuity formula and is:

      Present\text{ }value=payment\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg]

In your problem you know:

  • Present value: $100,000
  • payment: $15,000
  • r: ?
  • t: 10

You cannot solve for r directly. You must guess a value and calculate the right side of the equation until to you find the rate that makes it equal to 100,000.

Try 5%:

       \$15,000\times \bigg[\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^{10}}\bigg]=\$115,826

Then, the rate of return is greater than 5%. After several trials you will find that the rate of return is 8.15%.

Since this rate is higher than 8%, which is what the company requires, this is a good investment.

5 0
3 years ago
If a company has 5 employees with annual salaries of 30000 50000 30000 80000 and 70000 respectively what is the mean annual sala
Marina86 [1]

The answer is 52,000.


You have to add all of the values and divide them by the number of values. In this case you would do 30,000 + 50,000 + 30,000 + 80,000 + 70,000 which equals 260,000 then you would divide that number by 5 since there are 5 values.

5 0
3 years ago
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