According to an avid aquarist, the average number of fish in a 20-gallon tank is 10, with a standard deviation of two. His friend, also an aquarist, does not believe that the standard deviation is two. She counts the number of fish in 15 other 20-gallon tanks. Based on the results that follow, do you think that the standard deviation is different from the two at the 5% level? Data: 11; 10; 10; 10; 10; 11; 11; 10; 11; 9; 7; 10; 11; 10; 11.Part (a)State the null hypothesis.H0: ? 2 < 22H0: ? 2 = 22 H0: ? 2 > 22H0: ? 2 ≠ 22Part (b)State the alternative hypothesis.Ha: ? 2 ≥ 22Ha: ? 2 ≤ 22 Ha: ? 2 = 22Ha: ? 2 ≠ 22Part (c)What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.) Part (d)State the distribution to use for the test.?214t14 t15?215Part (e)What is the test statistic? (Round your answer to two decimal places.) =Part (f)What is the p-value? (Round your answer to four decimal places.) =Explain what the p-value means for this problem.If H0 is false, then there is a chance equal to the p-value of not obtaining a sample standard deviation equal to the one calculated or more extreme.If H0 is false, then there is a chance equal to the p-value of obtaining a sample standard deviation equal to the one calculated or more extreme. If H0 is true, then there is a chance equal to the p-value of not obtaining a sample standard deviation equal to the one calculated or more extreme .If H0 is true, then there is a chance equal to the p-value of obtaining a sample standard deviation equal to the one calculated or more extreme.Part (g)Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. Part (h)Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)? = (ii) Decision:reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision:Since ? < p-value, we reject the null hypothesis.Since ? > p-value, we reject the null hypothesis. Since ? > p-value, we do not reject the null hypothesis.Since ? < p-value, we do not reject the null hypothesis.(iv) Conclusion:There is sufficient evidence to support the claim that the standard deviation is not equal to 2.There is not sufficient evidence to support the claim that the standard deviation is not equal to 2.

Let σ be the population standard deviation. Given that, Population standard deviation (σ)=2Sample…

Answered: Based on the results that follow, do…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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According to an avid aquarist, the average number of fish in a 20-gallon tank is 10, with a standard deviation of two. His friend, also an aquarist, does not believe that the standard deviation is two. She counts the number of fish in 15 other 20-gallon tanks. Based on the results that follow, do you think that the standard deviation is different from the two at the 5% level? Data: 11; 10; 10; 10; 10; 11; 11; 10; 11; 9; 7; 10; 11; 10; 11.

Part (a)

State the null hypothesis.

H₀: ?² < 2²

H₀: ?² = 2²

H₀: ?² > 2²

H₀: ?² ≠ 2²
Part (b)

State the alternative hypothesis.

H_a: ?² ≥ 2²

H_a: ?² ≤ 2²

H_a: ?² = 2²

H_a: ?² ≠ 2²
Part (c)

What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)
Part (d)

State the distribution to use for the test.

?²₁₄

t₁₄

t₁₅

?²₁₅
Part (e)

What is the test statistic? (Round your answer to two decimal places.)
=
Part (f)

What is the p-value? (Round your answer to four decimal places.)

=
Explain what the p-value means for this problem.

If H₀ is false, then there is a chance equal to the p-value of not obtaining a sample standard deviation equal to the one calculated or more extreme.

If H₀ is false, then there is a chance equal to the p-value of obtaining a sample standard deviation equal to the one calculated or more extreme.

If H₀ is true, then there is a chance equal to the p-value of not obtaining a sample standard deviation equal to the one calculated or more extreme .

If H₀ is true, then there is a chance equal to the p-value of obtaining a sample standard deviation equal to the one calculated or more extreme.
Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.
Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:

reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:

Since ? < p-value, we reject the null hypothesis.

Since ? > p-value, we reject the null hypothesis.

Since ? > p-value, we do not reject the null hypothesis.

Since ? < p-value, we do not reject the null hypothesis.

(iv) Conclusion:

There is sufficient evidence to support the claim that the standard deviation is not equal to 2.

There is not sufficient evidence to support the claim that the standard deviation is not equal to 2.

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