An insurance company reports that 75% of its claims are settled within two months of being filed. In order to test that the percent is less than seventy-five, a state insurance commission randomly selects 35 claims and determines that 23 of the 35 were settled within two months.

a) Write out the hypotheses.

b) Calculate the test statistic.

c) Find the p-value.

d) Do we reject the null hypothesis? Explain.

e) What can you conclude based on this evidence

An insurance company reports that 75% of its claims are settled within two months of being filed. In order to test that the percent is less than seventy-five, a state insurance commission randomly selects 35 claims and determines that 23 of the 35 were settled within two months.

a) Write out the hypotheses.

Fewer than 75% of claims settled within two months of filing.

b) Calculate the test statistic.

Test statistic = percent of claims settled in two months = 23/35 = 65.7%

c) Find the p-value.

we need to use the z-score with a table

=  

standard deviation = s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2}, =

√(1/34) [(0.657)(12) + (0.343)(23)] = √0.463911765 = 0.681

let 1 = "solved" and 0 = "unresolved"

thus our mean is 0.657

z = (0.75 - 0.657)/(0.681) - 0.137

p = 0.55172

d) Do we reject the null hypothesis? Explain.

Yes, because our p value is not below 0.05 and is not substantial to prove our null hypothesis

e) What can you conclude based on this evidence?

That further testing is needed.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is