Hurricane Andrew swept through southern Florida causing billions of dollars of damage. Because of the severity of the storm and the type of residential construction used in the semitropical area, there was some concern that the average claim size would be greater than the historical average hurricane claims of $24,000. Several insurance companies collaborated in a data gathering experiment. They randomly selected 84 homes and sent adjusters to settle the claims. In the sample of 84 homes, the average claim was $27,5000 with a population standard deviation of $2400. Is there sufficient evidence at a 0.02 significance level to support the claim that the home damage is greater than the historical average? Assume the population of insurance claims is approximately normally distributec. Compute the value of the test statistic.

Question

25-07-2022
Mathematics

contestada

Hurricane Andrew swept through southern Florida causing billions of dollars of damage. Because of the severity of the storm and the type of residential construction used in the semitropical area, there was some concern that the average claim size would be greater than the historical average hurricane claims of $24,000. Several insurance companies collaborated in a data gathering experiment. They randomly selected 84 homes and sent adjusters to settle the claims. In the sample of 84 homes, the average claim was $27,5000 with a population standard deviation of $2400. Is there sufficient evidence at a 0.02 significance level to support the claim that the home damage is greater than the historical average? Assume the population of insurance claims is approximately normally distributec. Compute the value of the test statistic.

Respuesta :

Otras preguntas

Leroy borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what time period did Leroy borrow the money? Remember, your answer

PLEASE HELP ASAP Jada made 10 cups of blueberry jam and divided the jam equally among 4 containers. How much jam went in each container? 2/5 OF A CUP 1/10 CUP 5

List 6 different mechanisms in the Rube Goldberg cartoon and predict the purpose of each. Does the mechanism change speed, force, torque, direction, or type of

What is 70 in Spanish

The graph shows the temperature y in a freezer x minutes after it was turned on. Five minutes after being turned on, the temperature was actually four degrees f

What seasons did Harriet lead her groups? Spring and Winter Summer and Winter Spring and Fall O Summer and Fall

Reluctance Robert Frost OUT through the fields and the woods And over the walls I have wended; I have climbed the hills of view And looked at the world, and

657.9 as a whole number

Describe an Autocratic Government

ogorwyne ogorwyne · Answer 1 · 2022-08-04T18:20:56+02:00

The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

The hypothesis formulation

H0: u = 24000

H1: u > 24000

This test is a right tailed test

we have n = 84 homes

bar x = 27500

s = 2400

Next we have to find the test statistic

The formula for this is given as

[tex]t = \frac{x-u}{s/\sqrt{n} }[/tex]

When we out in the values we would have

[tex]t = \frac{27500-24000}{2400/\sqrt{84} }[/tex]

This would give us the answeer of the t test as

t test = 13. 3658

We have alpha = 0.02

the degree of freedom = 84 - 1 = 83

we have to find tα/2, df

= ±2.0865

Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.

Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.