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Calculation: We used the chi-square distribution to test the hypotheses. Assuming that, it is normal population distribution.
The population standard deviation, ${\sigma }^2={0.55}^2=0.3025$, with sample size, $n=10$.
The sample standard deviation s of x, can be calculated by using Excel as follows:
Step 1: Enter data of x1 in cell A1 to A10.
Step 2: Use command STDEV(A1:A10).
Therefore, the obtained sample standard deviation $s\approx 0.602$
The chi-square test statistic is calculating as:
$x^2=\frac{(n-1)s^2}{{\sigma }^2}=\frac{(10-1)(0.602{)}^2}{{0.55}^2}=10.78$
Degrees of fredom for $x^{2}is(n-1)$
$d.f=n-1$
$=10-1=9$
Conclusion:Assume the normal population distribution. $x^2$ statistic 10.78 with 9 degrees of freedom.