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 thatit will hold temperatures closer to 25°F. One frozen food case wasequipped with the new thermostat, and a random sample of 26temperature readings gave a sample variance of 4.7. Another similarfrozen food case was equipped with the old thermostat, and a randomsample of 14 temperature readings gave a sample variance of 12.2.Test the claim 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 ??₂²H₀:?₁² =?₂²; H₁:?₁² >?₂²    H₀:?₁² >?₂²; H₁:?₁² =?₂²H₀:?₁² =?₂²; H₁:?₁² <?₂²

(b) Find the value of the sample F statistic. (Round youranswer to two decimal places.)


What are the degrees of freedom?

dfN	=
dfD	=

What assumptions are you making about the originaldistribution?

The populations follow independent chi-square distributions. Wehave random samples from each population.The populations followdependent normal distributions. We have random samples from eachpopulation.    The populations followindependent normal distributions.The populations follow independentnormal distributions. We have random samples from eachpopulation.

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

p-value > 0.1000.050 < p-value <0.100    0.025 < p-value <0.0500.010 < p-value < 0.0250.001 <p-value < 0.010p-value < 0.001

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

At the ? = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.At the? = 0.05 level, we reject the null hypothesis and concludethe data are not statisticallysignificant.    At the ? = 0.05 level,we fail to reject the null hypothesis and conclude the data arestatistically significant.At the ? = 0.05 level, we failto reject the null hypothesis and conclude the data are notstatistically significant.

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

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 sufficientevidence that the population variance is larger in the oldthermostat temperature readings.    Reject thenull hypothesis, there is insufficient evidence that the populationvariance is larger in the old thermostat temperature readings.Failto reject the null hypothesis, there is insufficient evidence thatthe population variance is larger in the old thermostat temperaturereadings.