5. The following are the packaging times from two shipping machines (in seconds per shipment):Machine A 42.1 41.3 42.4 43.2 41.8 41.0 41.8 42.8 42.3 42.7Machine B 42.7 43.8 42.5 43.1 44.0 43.6 43.3 43.5 41.7 44.1Assuming these data represent random samples from normal populations, examine the hypothesis of equalvariances. Clearly state all the elements of the test, including your conclusion and its justification.

The data shows the packaging times for two shipping machines.Let σ12 be the population variance of machine A, and σ22 be the population variance of machine B. The hypothesis is, Null hypothesis: H0:σ12=σ22 Alternative hypothesis: H1:σ12≠σ22 The sample mean for machine A is, x¯1=∑X1n=42.1+41.3+⋯+42.710=421.410=42.14 The sample variance for machine A is, s12=∑X1-x¯12n-1=42.1-42.142+41.3-42.142+⋯+42.7-42.14210-1=4.2049=0.4671 The sample mean for machine B is, x¯2=∑X2n=42.7+43.8+⋯+44.110=432.310=43.23 The sample variance for machine B is, s22=∑X2-x¯22n-1=42.7-43.232+43.8-43.232+⋯+44.1-43.23210-1=5.0619=0.5623 Since the the variance for machine B is higher. The test statistic is, F=s22s12=0.56230.4671=1.1396 The test statistic is 1.1396. The degrees of freedom is, df=n1-1,n2-1=10-1,10-1=9,9 By using the EXCEL, the p-value is, The p-value is 0.8488. Since the p-value is very large indicating that the null hypothesis is not rejected. Thus, there is sufficient evidence to conclude that there is equal variances.