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

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

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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:
$$x^{2}=\frac{(n-1)s^{2}}{\sigma^{2}}=\frac{(10-1)(0.602)^{2}}{0.55^{2}}=10.78$$
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.