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Sagot :
Answer:
The answer is "yes".
Step-by-step explanation:
Given:
[tex]n= 25\\\\s = 0.0025\\\\\sigma_{0}= 0.005\\\\\alpha=0.01\\\\[/tex]
Claim:
[tex]\sigma < 0.42[/tex]
Its assertion is the null presumption or the alternative. The hypothesis should include the equal value of the claim. If indeed the claim is indeed the null assumption, the alternative hypothesis is indeed the opposite.
[tex]H_o: \sigma =0.42\\\\H_1 : \sigma<0.42[/tex]
Calculating the test statistic:
[tex]X^2=\frac{n-1}{\sigma_{0}^2} s^2=\frac{25-1}{0.005^2} \times 0.0025^2 \approx 6[/tex]
The key value of the left-tails test is shown in the row [tex]df = n -1=25-1 = 24[/tex] and the column with [tex]1 -\alpha = 0.99[/tex] in an appendix, from the chi-square table:
[tex]X_{1-\alpha}^{2}= 10.856[/tex]
All values are smaller than 10.856 in the reject region.
Unless the test statistic is in the refusal region, this same null hypothesis is rejected:
[tex]6 < 10.856 \to Reject \ H_{0}[/tex]
Its claim that perhaps the recalibration is efficient is demonstrated by sufficient evidence.
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