7) Here is a single randomly generated sample of n = 5 from a Normal distribution having mean of 10 and standard deviation of 2:6.477.5110.1013.639.91Although we know the true value of ], suppose that we pretend that we do not know it and want to test the following hypotheses:Ho: 0 = 8Ha: 00I 8a) Calculate the z statistic and its corresponding P-value.b) Is the test significant at the 5% level?c) Explain why this result is not surprising.

Name: 7) Here is a single randomly generated sample of n = 5 from a Normal
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Description: 7) Here is a single randomly generated sample of n = 5 from a Normal distribution having mean of 10 and standard deviation of 2:6.477.5110.1013.639.91Although we know the true value of ], suppose that we pretend that we do not know it and want to te

X (X-xbar)^2 6.47 9.326916 7.51 4.056196 10.1 0.331776 13.63 16.85924 9.91 0.148996…

Answered: 7) Here is a single randomly generated…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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7) Here is a single randomly generated sample of n = 5 from a Normal distribution having mean of 10 and standard deviation of 2:
6.47
7.51
10.10
13.63
9.91
Although we know the true value of ], suppose that we pretend that we do not know it and want to test the following hypotheses:
Ho: 0 = 8
Ha: 00I 8
a) Calculate the z statistic and its corresponding P-value.
b) Is the test significant at the 5% level?
c) Explain why this result is not surprising.

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X	(X-xbar)^2
6.47	9.326916
7.51	4.056196
10.1	0.331776
13.63	16.85924
9.91	0.148996

The mean is given by

$\overline{x} = \frac{1}{n}\sum x$
$\overline{x} = \frac{47.62}{5} =9.524$

The standard deviation is given by

$\sigma =\sqrt{\frac{1}{n-1}\sum (x - \overline{x})^2}$
$\sigma =\sqrt{\frac{30.723}{4}} =2.7714$

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