## Testing Variances Between ThermostatsA new thermostat has been engineered for frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable, maintaining temperatures closer to 25°F. One frozen food case with the new thermostat recorded a sample variance of 0.5 from 26 temperature readings. Another similar case with the old thermostat recorded a sample variance of 1.3 from 14 temperature readings. This task is to test if the population variance of the old thermostat's temperature readings is larger than the new one's.### Problem Statement- **Null and Alternative Hypotheses** - \( H_0: \sigma_1^2 = \sigma_2^2; H_1: \sigma_1^2 > \sigma_2^2 \)### Level of Significance- **(a)** What is the level of significance? - **5%** level of significance### Statistical Calculations- **(b)** Find the value of the sample F statistic. (Round to two decimal places.)- **Degrees of Freedom** - \( df_N = \) - \( df_D = \)### Assumptions About the Distribution- The populations follow independent normal distributions. We have random samples from each population.### P-Value Estimation- **(c)** Find or estimate the P-value of the sample test statistic. (Round to four decimal places.)### Hypothesis Testing- **(d)** Based on your calculations, will you reject or fail to reject the null hypothesis? - At the \(\alpha = 0.05\) level, we reject the null hypothesis if the data are statistically significant.### Interpretation and Conclusion- **(e)** Interpret your conclusion in the context of the application. - Reject the null hypothesis if there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.

(a) What is the level of significance? State the null and alternate hypotheses. O Họ: o? - 0?; Hạ:? > oz? O Họ: og? > az2; H: 0,? = 0z? O Họ: a,? - o3?; Hạ: a,? < oz? (b) Find the value of the sample F statistic. (Round your answer to two decimal places.) What are the degrees of freedom? dfo What assumptions are you making about the original distribution? O The populations follow independent normal distributions. O The populations follow independent chi-square distributions. We have random samples from each population. O The populations follow dependent normal distributions. We have random samples from each population. O The populations follow independent normal distributions. We have random samples from each population. (e) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? O At the a - 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the a - 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. O Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings. O Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings. O Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings. O Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.