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.

what