A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.
Single Policyholders Married Policyholders
n1 = 500 n2 = 800
Number making claims = 95 Number making claims = 80
(a) Use a level of significance a = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.
(b) Provide a 95% confidence interval for the difference between the proportions for the two populations.

Answer:

a

The  determination is  

    There is sufficient to conclude that proportion of the single policy

b

  The 95% confidence interval is  [tex] 0.0498    < p_1 - p_2 < 0.1302 [/tex]  

holders is difference from the proportion of married policy holders

Step-by-step explanation:

From the question we are told that

The sample size for single policy holders is [tex]n_1 = 500[/tex]

The number of single police holders making claim is k = 95

The sample size for married policy holders [tex]n_2 = 800[/tex]

The number of double police holders making claim is u = 80

The level of significance is [tex]\alpha = 0.05[/tex]

Generally the critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the

normal distribution table is

[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The null hypothesis is [tex]H_o : p_1 = p_2[/tex]

The alternative hypothesis is [tex]H_a : p_1 \ne p_2[/tex]

The sample proportion of single police holders making claim is

[tex]\r p_ 1 = \frac{k}{n_1}[/tex]

=> [tex]\r p_ 1 = \frac{95}{500}[/tex]

=> [tex]\r p_ 1 = 0.19[/tex]

The sample proportion of married police holders making claim is

[tex]\r p_ 2 = \frac{u}{n_2}[/tex]

=> [tex]\r p_ 2 = \frac{80}{800}[/tex]

=> [tex]\r p_ 2 = 0.1[/tex]

Generally the pooled sample proportion is mathematically represented as

[tex]\r p = \frac{k + u}{n_1 + n_2}[/tex]

=> [tex]\r p = \frac{95 + 80}{500 + 800}[/tex]

=> [tex]\r p = 0.1346 [/tex]

Generally the test statistics is mathematically represented as

[tex]z = \frac{\r p_1 - \r p_2 }{ \sqrt{ \r p (1 - \r p )* [\frac{1}{n_1} + \frac{1}{n_2} ]} }[/tex]

=> [tex]z = \frac{0.19 - 0.1 }{ \sqrt{0.1346 (1 - 0.1346 )* [\frac{1}{500} + \frac{1}{800} ]} }[/tex]

=>[tex]z = 4.6256 [/tex]

Generally the p-value is mathematically represented as

[tex]p-value = 2* P(Z >4.6256 )[/tex]

From the z table [tex]P(Z >4.6256 ) = 0 [/tex]

[tex]p-value = 2* 0 = 0[/tex]

From the calculation we see that the p-value < [tex]\alpha[/tex] so the null hypothesis is rejected

Hence there is sufficient to conclude that proportion of the single policy holders is difference from the proportion of married policy holders

Generally the standard error is mathematically represented as

[tex]SE = \sqrt{ \frac{\r p_1 (1 -\r p_1)}{n_1} + \frac{\r p_2 (1 -\r p_2)}{n_2} }[/tex]

=> [tex]SE = \sqrt{ \frac{0.19 (1 -0.19)}{500} + \frac{ 0.1 (1 - 0.1)}{800} }[/tex]

=> [tex]SE =0.0205012[/tex]

Generally the margin of error is mathematically represented as

[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]

=> [tex]E = 1.96 *0.0205012 [/tex]

=> [tex]E = 0.0402035[/tex]

Generally the 95% confidence level is mathematically represented as

[tex]\r p_1 - \r p_2 - E < p_1 - p_2 < \r p_1 - \r p_2 + E[/tex]

=> [tex]0.19  - 0.10 -0.0402035    < p_1 - p_2 < 0.19  - 0.10 + 0.0402035  [/tex]

=>  [tex]0.09 -0.0402035    < p_1 - p_2 < 0.09 + 0.0402035  [/tex]

=> [tex] 0.0498 < p_1 - p_2 < 0.1302 [/tex]

The length of the window is 2m longer than its width and the are is 32m²

Write the
slope-intercept form
of the equation of the
line described:

Perpendicular to y=x+4 and passes through the point (2,2)

add the following conceptually and using the standard algorithm 79-26​

What is the length of the hypotenuse of the triangle?

Which of the following completes the statement?

In the number 45,569, the 5 in the hundreds place is ______ the 5 to its left.

A. the same value as
B. 1/10 the value of
C. 10 times the value of
D. 100 times the value of ​

A selective college would like to have an entering class of 1200. Because not all students who are offered admission accept, the college admits more than 1200 students. Past experience shows that about 70% of the students will accept. The college decides to admit 1500 students. Assuming that students make their decision independently, the number who accept, X, has the Bin(1500, 0.70) distribution. If this number is lower than 1200, the college will admit students from its waiting list.What is the mean of the distribution of X - that is, the expected number of students who will accept admission

plz plz pls help pls

solve the proportion just type in the answer do not include the variables 14/8 equals x over 20​

What's the number of people left to play at 10 of
15 have played

What is the completely factored form of 3x5 – 7x4 + 6x2 – 14x?
(x Superscript 4 Baseline + 2 x) (3 x minus 7)
x Superscript 4 Baseline (3 x minus 7) (2 x minus 1)
x (x cubed + 2) (3 x minus 7)
x (3 x Superscript 4 Baseline minus 7 x cubed + 6 x minus 14)

A menagerie consists of seven brown dogs, two black dogs, six gray cats, ten black cats, five blue birds, six yellow birds, and one black bird. Deter- mine which of the following statements are true and which are false.
a. There is an animal in the menagerie that is red.
b. Every animal in the menagerie is a bird or a mammal.
c. Every animal in the menagerie is brown or gray or black.
d. There is an animal in the menagerie that is neither a cat nor a dog.
e. No animal in the menagerie is blue.
f. There are in the menagerie a dog, a cat, and a bird that all have the same color.

Someone, please help me out here.


P.S if you don't know the answer to this question don't comment at all because it's not very useful to me or anyone who needs help. Plus it just adds a warning to your account which may or may not get you banned.

When Louisa arranges her pennies into a rectangle with two equal rows, three equal rows, four equal rows, or six equal rows, she has one leftover penny. When she arranges her pennies into a rectangle with five equal rows, she has two leftover pennies. How many pennies could Louisa have? Remember he has between 10 and 40 pennies total.

what does it mean by "determine the equation of a line that passes through the given point. First find the slope" someone please help and give answer ASAP

The transformation function rule (x, y) --> (x - 1, y) is an example of which type of transformation?

Which expression is equivalent to 1/4 -3/4 x?

What is the y-intercept of the function f(x) =-2/9x + 1/3?
-2/9
-1/3
1/3
2/9

Factor 5x^2? + 10x + 2x + 4.​

R
(x + 1)
(3x - 5)
S
Р
What is mzPQR ?

What is a possible first step when multiplying 4/5 by 3

4/3+1/6=p what two numbers does p fall between

mia has 14 coins in her pocket that total $1.10. what are the coins in her pocket

The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For restaurants located in Boston, the average price of a dinner, including one drink and tip, was . You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed . Suppose that you randomly select three of these restaurants for dinner. a. What is the probability that none of the meals will exceed the cost covered by your company (to 4 decimals)

Solve by using the quadratic formula: x^2 - 6x + 7 = 0 Please enter any square root values using "sqrt" or the decimal answer rounded to the nearest hundredth (i.e. V2 = sqrt(2) or 1.41).​

What is 1/6 in a Percent

in general how does perimeter "a" affect y=a(b x-c)?​

is 9.90 biger or less or equal 9.9​

please help me with functions​

3
1
1 point
Solve the equation below. Round your answer to the nearest hundredth (2 decimal places) if needed.
4
X/15 +15=19
Type your answer.
5

6 eggs weigh 3/4 of a pound. How much does each egg weigh?