A company produces electric devices operated by a thermostatic control. The standard deviation of the temperature at which these controls actually operate should not exceed 2.0 degrees Fahrenheit. For a random sample of 20 of these controls the sample standard deviation of operating temperatures was 2.36 degrees Fahrenheit. Test at the 5% level the null hypothesis that the population standard deviation is 2.0 against the alternative that it is bigger
\[H_0 : \sigma \le 2.0 \\ H_1 : \sigma > 2.0\] Reject\[H_0\]if \[x^2 > x_{24,0.05}^{2} = 36.42\] Test statistic:\[x^2 = \frac{(n - 1)s^2}{\sigma_{0}^{2}} = \frac{(24)(2.36)^2}{(2)^2} = 33.418\] Therefore, we fail to reject \[H_0\]. We can conclude that the population standard deviation is at most 2 degrees Fahrenheit.
null hypothesis is sigma^2(le) 4 the alternate hypothesis is sigma^2(ge) 5.56 n=20 using x^2 (chi square test \[chi^2=(n-1)s^2/sigma^2=(19)(2.36)^2/(2)^2\] \[=26.45\] critical value from the table is 10.12 since 26.5 is gretor than critical value 10.26 reject the null hypothesis and accept the alternate
@failmathmajor you used n=25 while given n=20
Sorry
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