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USUULUYP43121bUOY-CV-WaUbben My OKstate Canvas b Billighway Geriatric Book UCO ASL Book 1 Spring 2020 Stat 2013/2053 - CRN 23
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Answer #1

Solution:

x x2
32 1024
30 900
29 841
28 784
27 729
26 676
25 625
22 484
21 441
47 2209
40 1600
35 1225
22 484
27 729
30 900
26 676
40 1600
\sumx=507 \sumx2=15927

The sample mean is \bar x

Mean \bar x = (\sumx / n) )


=32+30+29+28+27+26+25+22+21+47+40+35+22+27+30+26+40/17

=507/17

=29.8235

The sample standard is S

  S =\sqrt{}( \sum x2 ) - (( \sum x)2 / n ) n -1

=\sqrt{}15927-(507)217/16

=\sqrt{}15927-15120.5294/16

=\sqrt{}806.4706/16

=\sqrt{}50.4044

=7.0996

Degrees of freedom = df = n - 1 = 17 - 1 = 16

At 98% confidence level the t is ,

\alpha = 1 - 98% = 1 - 0.98 = 0.02

\alpha / 2 = 0.02 / 2 = 0.01

t\alpha /2,df = t0.01,16 =2.583

Margin of error = E = t\alpha/2,df * (s /\sqrtn)

= 2.583* (7.10 / \sqrt 17)

= 4.45

Margin of error = 4.45

The 98% confidence interval estimate of the population mean is,

\bar x - E < \mu < \bar x + E

29.82 - 4.45 < \mu < 29.82 + 4.45

25.37 < \mu < 34.27

(25.37, 34.27 )

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