Happy Life Financial, Inc. is an Ontario-based financial services company known primarily as a life insurance company. It is one of the largest life insurance companies in North America, and also one of the oldest with the history spanning back to 1891, when it was founded by Isaac Klein and Brian Cooper. Happy Life Financial has a strong presence in investment management with over CAD$100 billion in assets under management operating in a number of countries all over the world.
Parul Jaiswal, a Humber College graduate who always had only perfect marks in statistics, was hired by the Etobicoke branch of Happy Life Financial in 2017. Parul was assigned to conduct statistical analysis of data, as well as market analysis. As Parul is on probation, please help her to complete the following tasks. For your convenience the data are given in the Major Assignment Data file. You can also find useful information on the Blackboard in Excel Instructions folder in the files Confidence Intervals and Hypothesis Testing with Excel parts I, II, and III.
1. Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Life expectancy is a statistical measure of average time a person is expected to live, based on a number of demographic factors. Mathematically, life expectancy is the mean number of years of life remaining at a given age, assuming age-specific mortality rates remain at their most recently measured levels.
Last year the average life expectancy of all Happy Life policyholders in Ontario at age 65 was 22.3 years (meaning that a person reaching 65 last year was expected to live, on average, until 87.3). Happy Life wants to determine if their clients now have a longer average life expectancy, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample is given in the Major Assignment Data file. Help Parul to answer questions a.- h. Answers to questions d.- h. should be supported by Excel output.
a. Write the null and alternative hypotheses for this test:
H0:
H1:
b. In this context, describe a Type I error possible. How might such an error impact Happy Life decision regarding the premium structure?
c. In this context, describe a Type II error possible. How might such an error impact Happy Life decision regarding the premium structure?
d. Construct a histogram for the given sample with bin values: 16, 18, 20, 22, 24, 26, 28, and 30. Does it look that the data come from a distribution that is unimodal and symmetric (approximately Normal) and therefore t-model is applicable as a data analysis tool?
e. What is the value of the t-test statistic?
f. What is the associated P-value?
g. State the conclusion using α = 0.05. Do it using both P-value and critical value.
h. Please reconsider the previous question at α = 0.01. Is your conclusion different? Why?
Policy Holder # Life Expectancy at 65 1- 20.4, 2- 22.2, 3- 17.6 4- 27.2 5 24.5 6 20.3 7 21.3 8 22.5 9 26.7 10 18.3 11 23.5 12 25.6 13 22.1 14 24.2 15 15.4 16 23.4 17 25.3 18 18.5 19 24.2 20 20.3 21 26.8 22 28.1 23 19.9 24 25.5 25 22.3 26 23.9 27 31.7 28 26.0 29 22.8 30 23.3 31 25.9 32 17.7 33 19.6 34 21.8 35 23.3 36 21.9 37 21.9 38 28.7 39 19.9 40 27.8 41 26.6 42 21.1 43 23.3 44 25.5 45 23.8 46 21.4 47 23.3 48 23.6 49 23.1 50 23.9