Step 1

Given,

\(n_{1} = 19, s_{1}^{2} = 12.8\)

\(n_{2} = 21, s_{2}^{2} = 5.1\)

Level of significance, \(\alpha = 0.05\)

Step 2

a)

Null Hypothesis \((H_{0}): \sigma_{1}^{2} = \sigma_{2}^{2}\)

Alternate Hypothesis \((H_{1}): \sigma_{1}^{2} > \sigma_{2}^{2}\)

b) F-statistic:

\(F = \frac{s_{1}^{2}}{s_{2}^{2}}\)

\(= 12.8/5.1= 2.51\)

\(df_{N} = 19 - 1 = 18\)

\(df_{D} = 21 - 1 = 20\)

c) P-value = 0 .0246

d) At \(\alpha = 0.05\) , we reject the null hypothesis and conclude the data are statistically significant. as p-value is less than significance level

e) Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings

Given,

\(n_{1} = 19, s_{1}^{2} = 12.8\)

\(n_{2} = 21, s_{2}^{2} = 5.1\)

Level of significance, \(\alpha = 0.05\)

Step 2

a)

Null Hypothesis \((H_{0}): \sigma_{1}^{2} = \sigma_{2}^{2}\)

Alternate Hypothesis \((H_{1}): \sigma_{1}^{2} > \sigma_{2}^{2}\)

b) F-statistic:

\(F = \frac{s_{1}^{2}}{s_{2}^{2}}\)

\(= 12.8/5.1= 2.51\)

\(df_{N} = 19 - 1 = 18\)

\(df_{D} = 21 - 1 = 20\)

c) P-value = 0 .0246

d) At \(\alpha = 0.05\) , we reject the null hypothesis and conclude the data are statistically significant. as p-value is less than significance level

e) Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings