Question

The 2010 insurance premiums from both Geico and 21st Century for a male driver licensed for 6–8 years who drives a Honda Accord 12,600 to 15,000 miles per year and has no violations are given in the table below. The table also indicates the city of residence. City Geico ($) 21st Century ($) Difference ($) Long Beach 2780 2352 Pomona 2411 2462 San Bernardino 2261 2284 Moreno Valley 2263 2520
(a) Fill in the entires in the difference column in the above table. (b) Compute the mean of the differences. (c) Verify that the sample standard deviation of the differences is s ≈288.68. (d) Compute the standard error of the differences, using n =4. (e) Using a significance level of α =0.01, do these data provide sufficient evidence to indicate that there is a difference in the premiums between Geico and 21st Century?

Answer 1

(a)

	City Geico ($)	21st Century ($)	Difference ($)
Long Beach	2780	2352	428
Pomona	2411	2462	-51
San Bernardino	2261	2284	-23
Moreno Valley	2263	2520	-257

(b)

Mean of the difference is,

(c)

Sample standard deviation of the difference is,

(d)

Standard error of the difference is,

(e)

The hypothesis are,

Ho : There is no difference in the premiums between Geico and 21st century.

Ha : There is difference in the premiums between Geico and 21st century.

The test statistics is,

t = Mean difference / Standard error of difference

t = 24.25/144.34

t = 0.168

Here, = 0.01 and df = n - 1 = 3

Using table of critical values for t-distribution the critical values are -5.841 and 5.841

Since test statistics value does not falls in the critical region, we fail to reject Ho.

Therefore, there is no sufficient evidence to indicate that there is difference in the premiums between Geico and 21st century.