A manager for an insurance company believes that customers have the following preferences for life insurance products: 40 % prefer Whole Life, 20 % prefer Universal Life, and 40 % prefer Life Annuities. The results of a survey of 212 212 customers were tabulated. Is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data?

state the null and alternative hypothesis

What does the null hypothesis indicate about the proportions of customers who prefer each insurance product?

State the null and alternative hypothesis in terms of the expected proportions for each category

Find the expected value for the number of customers who prefer Whole Life. Round your answer to two decimal places.

Find the expected value for the number of customers who prefer Life Annuities. Round your answer to two decimal places.

Find the value of the test statistic. Round your answer to three decimal places.

Find the degrees of freedom associated with the test statistic for this problem.

Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance

State the conclusion of the hypothesis test at the 0.01 level of significance

An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company: First birthday: $ 760 Second birthday: $ 760 Third birthday: $ 860 Fourth birthday: $ 860 Fifth birthday: $ 960 Sixth birthday: $ 960 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $360,000.

If the relevant interest rate is 12 percent for the first six years and 7 percent for all subsequent years, what is the value of the policy at the child's 65th birthday? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Child's 65th birthday $

An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company: First birthday $ 880 Second birthday 880 Third birthday 980 Fourth birthday 850 Fifth birthday 1,080 Sixth birthday 950 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $380,000. If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, what would the value of the deposits be when the policy matures? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $

An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child’s birth. For this policy, the purchaser, say, the parent, makes the following six payments to the insurance company:

First birthday $ 820

Second birthday $ 820

Third birthday $ 920

Fourth birthday $ 850

Fifth birthday $ 1,020

Sixth birthday $ 950

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $320,000. If the relevant interest rate is 10 percent for the first six years and 7 percent for all subsequent years, what would the value of the deposits be when the policy matures? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company: First birthday: $750 Second birthday: 750 Third birthday: 850 Fourth birthday: 850 Fifth birthday: 950 Sixth birthday: 950 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $500,000. If the relevant interest rate is 10 percent for the first six years and 8 percent for all subsequent years, is the policy worth buying?

A petroleum company fills large drums of oil to distribute to customers. In a random sample of 35 drums, the mean number of gallons of oil is 202.52 and the standard deviation is 1.23. The company would like to ensure its customers that the average number of gallons of oil in the drums that the company distributes is greater than 200 gallons. We will conduct a statistical test to evaluate this claim.

1. Formulate the null hypothesis (in words) to evaluate this claim.

2. Formulate the alternative hypothesis (in words) to evaluate this claim.

3. What is μ0 in the statistical test?

4. What is the population parameter that the statistical test is concerned with?

5. Which sample statistic can be used to estimate the population parameter that the statistical tests is testing?

6. Is using the parametric tests discussed in class applicable? Explain why or why not.

7. What values of x̄ would lead you to reject the null hypothesis at a confidence level of 90%?

   Calculate this based on the t-test and z-test.

8. What values of x̄ would lead you to reject the null hypothesis at a confidence level of 95%?

   Calculate this based on the t-test and z-test.

9. What values of x̄ would lead you to reject the null hypothesis at a confidence level of 99%?

   Calculate this based on the t-test and z-test.

   x̄−μ0

10. Suppose we transform x̄ into the test statistic T = s/√n . What values of T would lead you

    to reject the null hypothesis at a confidence level of 90%? Calculate this based on the t-test and z-test.

    x̄−μ0

11. Suppose we transform x̄ into the test statistic T = s/√n . What values of T would lead you

    to reject the null hypothesis at a confidence level of 95%? Calculate this based on the t-test and z-test.

    x̄−μ0

12. Suppose we transform x̄ into the test statistic T = s/√n . What values of T would lead you

    to reject the null hypothesis at a confidence level of 99%? Calculate this based on the t-test and z-test.

13. What is the p-value of this test? Calculate it based on x̄ and also based on the transformed statistic, using both the t and normal distributions.

14. What is the minimum confidence level for which you would reject the null hypothesis? Answer this using the p-values for both the t and normal distribution.

Your company maintains a database with information on your customers, and you
are interested in analyzing patters observed over the past quarter. 23% of customer
in the database placed new orders within this period. However, for those customers
who had a salesperson assigned to them, the new order rate was 58%. Overall, 14%
of customers within the database had salesperson assigned to them.
a) Draw a contingency table for this situation.
b) What percentage of customers in the database placed a new order but did not
have a salesperson assigned to them.
c) Given that a customer did not place a new order, what is the probability that the
customer had a salesperson assigned to him or her?
d) If a customer did not have a salesperson assigned to him or her, what is the
probability that the customer placed a new order?

A manager for an insurance company believes that customers have the following preferences for life insurance products: 40% prefer Whole Life, 20% prefer Universal Life, and 40% prefer Life Annuities. The results of a survey of 209 customers were tabulated. Is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data? Product Number Whole 86 Universal 54 Annuities 69 Step 4 of 10: Find the expected value for the number of customers who prefer Whole Life. Round your answer to two decimal places. Step 5 of 10: Find the expected value for the number of customers who prefer Universal Life. Round your answer to two decimal places. Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places. Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem. Step 8 of 10: Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places. Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.025 level of significance. Step 10 of 10: State the conclusion of the hypothesis test at the 0.025 level of significance.

4. A manager for an insurance company believes that customers have the following preferences for life insurance products: 40% prefer Whole Life, 30% prefer Universal Life, and 30% prefer Life Annuities. The results of a survey of 320 customers were tabulated. Is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data?

Product   Number
Whole         24
Universal   96
Annuities   200

Step 1 of 10: State the null and alternative hypothesis.

H0: Preferences for life insurance products are as per the manager's belief.

Ha: Preferences for life insurance products are not as per the manager's belief.

or

H0: Preferences for life insurance products are not as per the manager's belief.

Ha: Preferences for life insurance products are as per the manager's belief.

Step 2 of 10: What does the null hypothesis indicate about the proportions of customers who prefer each insurance product?

a. The proportions of customers who prefer each insurance product are all thought to be equal.
b. The proportions of customers who prefer each insurance product are different for each category (and equal to the previously accepted values).

Step 3 of 10: State the null and alternative hypothesis in terms of the expected proportions for each category.

P whole=

P universal=

P annuities =

Step 4 of 10: Find the expected value for the number of customers who prefer Whole Life. Round your answer to two decimal places.

E( whole) =

Step 5 of 10: Find the expected value for the number of customers who prefer Life Annuities. Round your answer to two decimal places.

E (annuities)

Step 6 of 10:Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem.

Step 8 of 10:Find the critical value of the test at the 0.05 level of significance. Round your answer to three decimal places.

Step 9 of 10:Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.

Step 10 of 10:State the conclusion of the hypothesis test at the 0.05level of significance.

a. There is not enough evidence to refute the manager's claim about the proportions of customers who prefer each product.
b. There is enough evidence to refute the manager's claim about the proportions of customers who prefer each product.