Q1 An insurance agent randomly selected 10 of his clients an

Q1 An insurance agent randomly selected 10 of his clients and checked online price quotes for their policies. His summaries of the data are shown, where Diff is Localminus?Online.

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Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to an online agent. Use ?=0.05.

Solution

An insurance agent randomly selected 10 of his clients and checked online price quotes for their policies.

Test of hypothesis is,

H0 : m_d = 0 Vs H1 :m_d 0

This is paired t-test.

alpha = 0.05

The test statistic is,

t = (Xbar - m_d) / s/sqrt(n)

where Xbar is mean of difference local - online

s is the standard deviation of difference local - online

n is he numbe of pairs.

m_d is the population mean which we have tested.

Paired t-test by using MINITAB is,

steps :

START --> STAT --> Basic statistics --> paired t --> samples in columns --> first sample : local --> second sample : online --> options : confidence level = 0.95 -->test mean = 0.0 --> alternative : not equal --> ok --> ok

These steps will gives us following output.

Paired T-Test and CI: local, online

Paired T for local - online

N Mean StDev SE Mean
local 10 954.200 345.972 109.406
online 10 888.200 338.693 107.104
Difference 10 66.0000 168.5929 53.3137

95% CI for mean difference: (-54.6041, 186.6041)
T-Test of mean difference = 0 (vs not = 0): T-Value = 1.24 P-Value = 0.247

The test statistic is 1.24.

P-value = 0.247

P-value > alpha

Accept H0 at 0.05 level of significance.

Conclude that mean difference is 0.