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

Question

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

anonymous · Answer

$$H_0 : \sigma \le 2.0 \ H_1 : \sigma > 2.0$$

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.

anonymous · Answer

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

anonymous · Answer

@failmathmajor  you used n=25 while given n=20

anonymous · Answer

Sorry

anonymous · Answer

thank you