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set
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Set of vowels in eng
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\bar x = 260.1615

x

ˉ

=260.1615

\sigma = 70.69σ=70.69

The confidence interval of standard deviation is: 53.7653.76 to 103.25103.25

Step-by-step explanation:

Given

n =20n=20

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

\bar x = \frac{\sum x}{n}

x

ˉ

=

n

∑x

So, we have:

\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 ++250.61}{20}

x

ˉ

=

20

242.87+212.00+260.93+284.08+194.19+139.16+260.76+436.72+355.36++250.61

\bar x = \frac{5203.23}{20}

x

ˉ

=

20

5203.23

\bar x = 260.1615

x

ˉ

=260.1615

\bar x = 260.16

x

ˉ

=260.16

Solving (b): The standard deviation

This is calculated as:

\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}σ=

n−1

∑(x−

x

ˉ

)

2

\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2++(250.61- 260.1615)^2}{20 - 1}}σ=

20−1

(242.87−260.1615)

2

+(212.00−260.1615)

2

+(260.93−260.1615)

2

+(284.08−260.1615)

2

++(250.61−260.1615)

2

\sigma = \sqrt{\frac{94938.80}{19}}σ=

19

94938.80

\sigma = \sqrt{4996.78}σ=

4996.78

\sigma = 70.69σ=70.69 --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

c =0.95c=0.95

So:

\alpha = 1 -cα=1−c

\alpha = 1 -0.95α=1−0.95

\alpha = 0.05α=0.05

Calculate the degree of freedom (df)

df = n -1df=n−1

df = 20 -1df=20−1

df = 19df=19

Determine the critical value at row df = 19df=19 and columns \frac{\alpha}{2}

2

α

and 1 -\frac{\alpha}{2}1−

2

α

So, we have:

X^2_{0.025} = 32.852X

0.025

2

=32.852 at \frac{\alpha}{2}

2

α

X^2_{0.975} = 8.907X

0.975

2

=8.907 --- at 1 -\frac{\alpha}{2}1−

2

α

So, the confidence interval of the standard deviation is:

\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} } to \sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }

70.69 * \sqrt{\frac{20 - 1}{32.852} to 70.69 * \sqrt{\frac{20 - 1}{8.907}

70.69 * \sqrt{\frac{19}{32.852} to 70.69 * \sqrt{\frac{19}{8.907}

53.7653.76 to 103.25103.25

4) read the following excerpt. cognitive psychology has been widely developed, not only in brazil, but also in the world. it studies human intellectual capacities, analyzing the ways in which people solve mental tasks, and construct models for understanding such processes, understood from the information processing paradigm. this occurs through basic and superior cognitive processes. is one of the basic cognitive processes, considered the gateway to the stimuli that will be processed cognitively. through it we can extract meanings from the external environment, either through vision or through hearing. check the alternative that fits the gap correctly. select an alternative: a) perception. b) attention. c) memory. d) consciousness. e) intelligence.