Lily Energy Systems manufactures wood-burning heaters and fireplace inserts.One of its systems has an electric blower,which is thermostatically controlled.The blower is designed to automatically turn on when the temperature in the stove reaches 125 degrees F.and turn off at 85 degrees F.Complaints from customers indicate that the thermostat control is not working properly.The company feels that the thermostat is acceptable if the variance in the cutoff temperature is less than or equal to 175.The company takes a sample of 24 thermostats and finds that the variance equals 289.The calculated chi-square test statistic and the table value for a 0.05 significance level are:
A) 35.172,38.99.
B) 37.983,35.172.
C) 38.076,38.99.
D) 37.983,38.076.
E) none of these.

Question

Quizplus · Accepted Answer

The chi-square test statistic can be calculated as follows:

χ2 = (n-1)s2 / σ2

where n is the sample size, s2 is the sample variance, and σ2 is the population variance (which we don't know).

In this case, n=24 and s2=289. We don't have a value for σ2, but we can estimate it by using the chi-square distribution with n-1 degrees of freedom. For a 0.05 significance level and 23 degrees of freedom, the table value is 35.172.

Plugging in the numbers, we get:

χ2 = (24-1)(289) / σ2 
χ2 / 23 = 12.565

Since 12.565 is greater than the table value of 35.172, we reject the null hypothesis that the variance in cutoff temperature is less than or equal to 175, and conclude that there is sufficient evidence to suggest that the thermostat control is not working properly.

Therefore, the best choice is B) 37.983,35.172.

Lily Energy Systems Manufactures Wood-Burning Heaters and Fireplace Inserts