Question

Summary statistics for 10​ drivers' car insurance premiums quoted by a local agent and an online company are shown in the table to the right. The accompanying table has displays for each​ company's quotes and for the difference.

Variable   Count   Mean   StdDev
Local   10   795.3   226.994
Online   10   732.7   303.131
Price Diff   10   62.6   173.762

Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company.

Identify the null and alternative hypotheses.

Calculate the test statistic.

Calculate the​ P-value.

State the conclusion. Assume alpha equals0.05.

Local   Online   PriceDiff
557   377   180
861   566   295
461   486   -25
1221   1133   88
600   638   -38
1013   1242   -229
776   450   326
843   802   41
913   1022   -109
708   611   97

Answer 1

Here we need to compare more than three population means so one way ANOVA will be used.

Hypotheses are:

H0: All companies have same average cost.

Ha: Not all companies have same average cost.

Hypotheses in symbol:

Following is the output of one way ANOVA:

The test statistics is

F = 28.51

The p-value is: 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis. That is there is evidence to conclude that  drivers might save money by switching to the online company.