Question

Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that auto insurance rates are normally distributed for both boys and girls, and the population standard deviation for each group is  = $180. At the .01 significance level, does this data provide evidence that the mean cost for auto insurance for teenage boys is greater than that for teenage girls?

work must include

1. Clear statement of hypotheses, with the correct parameter(s)
2. An indication of the test used
3. The test statistic and p-value
4. An indication of the statistical decision (i.e. whether or not to reject Ho)
     along with an explanation.
5. An interpretation of the statistical decision in the context of the problem.  

Answer 1

Answer:

Given,

sample n1 = 36 , n2 = 23

x1 = 679 , x2 = 559

standard deviation = s1 = 180 , s2 = 180

Null hypothesis Ho : u1 = u2

Alternative hypothesis Ha : u1 > u2

test statistic z = (x1 - x2)/sqrt(s1^2/n1 + s2^2/n2)

substitute values

= (679 - 559)/sqrt(180^2/36 + 180^2/23)

= 2.50

significance level = 0.01

Here at 99% CI, z value is 2.58

Here zcal < 2.58, so we fail to reject Ho.

So there is no sufficient evidence.