Explained: "Check Requirements What sampling distribution will you use?..."

Wierzycaz

Answered question

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?

Answer & Explanation

Alix Ortiz

Skilled2021-02-03Added 109 answers

Calculation: We used the chi-square distribution to test the hypotheses. Assuming that, it is normal population distribution.
The population standard deviation,

σ^{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}}{σ^{2}} = \frac{(10 - 1) (0.602)^{2}}{{0.55}^{2}} = 10.78

Degrees of fredom for

x^{2} i s (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.

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