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natulia [17]
3 years ago
11

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher

estimated the population mean and population standard deviation from a sample of 500 observations.
In addition, the researcher used 6 standardized intervals to test for normality.

Using a 5% level of significance, the critical value for this test is:

a. 11.1433.
b. 9.3484.
c. 7.8147.
d. 9.4877.
Mathematics
1 answer:
marta [7]3 years ago
8 0

Answer:

Solution: C) 7.815

Hint: From Chi-square table with (k-r-1)=(6-2-1) = 3 d.f the critical value = 7.8147

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Find the radius of convergence, then determine the interval of convergence
galben [10]

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.  

<h3>Find the radius of convergence R and the interval of convergence:</h3>

Ratio test is the test that is used to find the convergence of the given power series.  

First aₙ is noted and then aₙ₊₁ is noted.

For  ∑ aₙ,  aₙ and aₙ₊₁ is noted.

\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }| = β

  • If β < 1, then the series converges
  • If β > 1, then the series diverges
  • If β = 1, then the series inconclusive

Here a_{k} = \frac{(x+2)^{k}}{\sqrt{k} }  and  a_{k+1} = \frac{(x+2)^{k+1}}{\sqrt{k+1} }

   

Now limit is taken,

\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }| = \lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|

= \lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|

= \lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|

= |{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}

= |{x+2 }| < 1

- 1 < {x+2 } < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

 

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

Learn more about radius of convergence here:

brainly.com/question/14394994

#SPJ1

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A manufacture inspects 800 light bulbs and finds that 796 of them have no defects. What is the experimental probability that a l
BartSMP [9]

Answer:

The experimental probability that a light build chosen at random has no defects is 99.5 % or P(A)=0.995.

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let S be the sample space for the inspection of the light bulbs.

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let ' A ' be the event of no defects bulbs.

Therefore, n(A) = 796

Now the Experiment probability for a light bulb chosen has no defects will be given by,

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Substituting the values we get

P(A)=\dfrac{796}{800}=0.995

The experimental probability that a light build chosen at random has no defects is 99.5 % or P(A)=0.995.

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I think it would be the third option. I jiust guessed.

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