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

Answer 1

\[H_0 : \sigma \le 2.0 \\ H_1 : \sigma > 2.0\]

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.

Answer 2

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

Answer 3

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

Answer 4

Sorry

Answer 5

thank you