Wierzycaz

2021-02-02

Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?

Alix Ortiz

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:
${x}^{2}=\frac{\left(n-1\right){s}^{2}}{{\sigma }^{2}}=\frac{\left(10-1\right)\left(0.602{\right)}^{2}}{{0.55}^{2}}=10.78$
Degrees of fredom for
$d.f=n-1$
$=10-1=9$
Conclusion:Assume the normal population distribution. ${x}^{2}$ statistic 10.78 with 9 degrees of freedom.

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