A new thermostat has been engineered for the frozen food casesin large supermarkets. Both the old and new thermostats holdtemperatures at an average of 25°F. However, it is hoped that thenew thermostat might be more dependable in the sense that it willhold temperatures closer to 25°F. One frozen food case was equippedwith the new thermostat, and a random sample of 26 temperaturereadings gave a sample variance of 5.1. Another similar frozen foodcase was equipped with the old thermostat, and a random sample of16 temperature readings gave a sample variance of 12.8. Test theclaim that the population variance of the old thermostattemperature readings is larger than that for the new thermostat.Use a 5% level of significance. How could your test conclusionrelate to the question regarding the dependability of thetemperature readings? (Let population 1 refer to data from the oldthermostat.)

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: ?12 = ?22; H1: ?12 < ?22

H0: ?12 = ?22; H1: ?12 ? ?22

H0: ?12 = ?22; H1: ?12 > ?22

H0: ?12 > ?22; H1: ?12 = ?22

(b) Find the value of the sample F statistic. (Round your answerto two decimal places.) What are the degrees of freedom?

dfN =

dfD = What assumptions are you making about the originaldistribution?

The populations follow independent normal distributions. We haverandom samples from each population.

The populations follow independent normal distributions. Thepopulations follow independent chi-square distributions. We haverandom samples from each population.

The populations follow dependent normal distributions. We haverandom samples from each population.

(c) Find or estimate the P-value of the sample test statistic.(Round your answer to four decimal places.)

p-value > 0.100

0.050 < p-value < 0.100

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.001 < p-value < 0.010

p-value < 0.001

(d) Based on your answers in parts (a) to (c), will you rejector fail to reject the null hypothesis?

At the ? = 0.05 level, we reject the null hypothesis andconclude the data are statistically significant.

At the ? = 0.05 level, we fail to reject the null hypothesis andconclude the data are not statistically significant.

At the ? = 0.05 level, we fail to reject the null hypothesis andconclude the data are statistically significant.

At the ? = 0.05 level, we reject the null hypothesis andconclude the data are not statistically significant.

(e) Interpret your conclusion in the context of theapplication.

Reject the null hypothesis, there is insufficient evidence thatthe population variance is larger in the old thermostat temperaturereadings.

Reject the null hypothesis, there is sufficient evidence thatthe population variance is larger in the old thermostat temperaturereadings.

Fail to reject the null hypothesis, there is sufficient evidencethat the population variance is larger in the old thermostattemperature readings.

Fail to reject the null hypothesis, there is insufficientevidence that the population variance is larger in the oldthermostat temperature readings.