Question 1

1. Indemnity insurance…

a. reimburses for certain types of losses such as accidents or theft.

b. is the basis for most of the health insurance coverage in the U.S.

c. is often “experience-rated” with premiums based on expected losses.

d. is sometimes called “casualty insurance.”

e. All of the above

Question 10

An insurance company initially is insuring a pool of 200 people, each of whom has a 5% chance of a $10,000 loss due to illness.

(III.) The insurer needs to charge a premium to each of the 200 people that is enough to fully cover the expected loss per person, plus an additional 8% “loading cost” to each person to cover all its operating expenses and generate a profit. How much does the premium per person have to be (in dollars)?

a. $540

b. $580

c. $625

d. $1,080

Question 12

An insurance company was initially insuring a pool of 200 people, each of whom has a 5% chance of a $10,000 loss due to illness.

In addition, a new, “high risk” group of 50 people is also being insured. Each of these 50 people has a 50% chance of the $10,000 loss.

(V.) Suppose the insurer must group everyone together into a single 250 person pool. If the insurer must now charge everyone the same premium, how much does it have to be (in dollars per person, including the 8% loading cost)?

a. $1,080

b. $1,400

c. $1,512

d. $5,940

There was an SRS of 100 flights on a large airline (airline 1) that showed that 64 of the flights were on time. An SRS of 100 flights of another large airline (airline 2) showed that 80 of the flights were on time. Let p₁ and p₂ be the proportion of all flights that are on time for these two airlines.

What is a 95% confidence interval for the difference p₁-p₂?

A manufacturer of sprinkler systems used in office buildings to protect against fires claims that its sprinklers are activated at a temperature of 130°F. The sample of 9 systems recorded the temperature at the time of activation of the system.

Temperature 133.90 132.15 130.23 129.23 133.45 131.94 130.18 130.82 129.77

Summary Statistics

Mean: 131.29667

Std Dev: 1.6496212

Std. Err

Mean: 05498737 N:9

a) Construct a 99% confidence interval for the mean temperature at activation. What does this interval mean?

b) Construct a 99% upper confidence interval for the mean temperature at activation.

c) What size sample is necessary to construct a 99% confidence interval with a margin of error of only 0.5°F?

d) Can you conclude the manufacturer’s claim is wrong? (Do a hypothesis test.) e) Can you trust the results from the statistical procedures in parts a through d? Are the results valid?

1. Is there a difference in the level of pain relief among patients with rib fractures who use painkilling drugs and those who use transcutaneous nerve stimulation (TENS)? A small study that involved 30 people with rib fractures was conducted in an orthopedic office. Usable data were collected from 23 of the patients. The outcome variable of interest is “level of pain: as rated by the patient on a scale from 0-20, where 0 is no pain relief and 20 is complete pain relief. The data:

Complete the appropriate test to answer the research question. To be done by hand.

.) Is the type of health care provider related to the patient’s satisfaction with care? Data are from a study of 10 patients who were seen for health care at an HMO. Each patient had three different urgent care visits. On one visit, the patient was seen by a physician (MD), at another visit by a nurse practitioner (NP), and at the third visit by a physician’s assistant (PA). After each visit, the patient completed a patient satisfaction survey. Satisfaction was measured by a 10-item scale, which returns scores from 0 to 10, with 0 indicating the least satisfied and 10 indication the most satisfied. The data:

          Complete the appropriate test by hand. If appropriate,   

         complete a Post Hoc test. (To be done by hand)

1. Does therapy combined with exercise alleviate depressive symptoms more than therapy alone? People who were newly diagnosed with mild depression were invited into the study. Study participants were carefully matched on age, race and gender. One person from each pair was assigned to the therapy alone group, and the other was assigned to the therapy plus exercise group. Twelve weeks later, the depression levels of the two groups were compared to see which of the two groups had a lower number of depressive symptoms. The data:

Complete the appropriate test to answer the research question. To be done by hand.

• What is the conservative critical F statistic if your sample size is 50 and you are comparing 3 groups of participants (at the .05 level)?
• What is the critical F statistic value for the following F (4,70), use a .05 level of significance?
• If you have an MS between of 3.1 and MS within groups of 0.3, what would your calculated F statistic be?
• If you saw the result of ANOVA like this F(2,40) = 4.5, how many groups were in the study and how many participants were in the study?

Give an example of when you would use a one-way ANOVA. What is dependent and what is independent variable?

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 427427 gram setting. It is believed that the machine is underfilling the bags. A 1515 bag sample had a mean of 421421 grams with a standard deviation of 2828. A level of significance of 0.050.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Let μ denote the true average lifetime for a certain type of pen under controlled laboratory conditions. A test of H₀: μ = 10 versus H_a: μ < 10 will be based on a sample of size 36. Suppose that σ is known to be 0.6, from which σ_x = 0.1. The appropriate test statistic is then

Answer the following questions using Table 2 in Appendix A.

(a) What is α for the test procedure that rejects H₀ if z ≤ -1.26? (Give answer to 4 decimal places.)
α =  

(b) If the test procedure of Part (a) is used, calculate β when μ = 9.8. (Give answer to 4 decimal places.)
β =

(c) Without doing any calculation, explain how β when μ = 9.5 compares to β when μ = 9.8.
β when μ = 9.5 would be  ---Select--- smaller larger  than β when μ = 9.8.

Check your assertion by computing β when μ = 9.5.
β =  

(d) What is the power of the test when μ = 9.8? (Give answer to 4 decimal places.)

Hypothesis testing is used in business to test assumptions and theories. These assumptions are tested against evidence provided by actual, observed data. A statistical hypothesis is a statement about the value of a population parameter that we are interested in. Hypothesis testing is a process followed to arrive at a decision between 2 competing, mutually exclusive, collective exhaustive statements about the parameter’s value.

Consider the following scenario: An industrial seller of grass seeds packages its product in 50-pound bags. A customer has recently filed a complained alleging that the bags are underfilled. A production manager randomly samples a batch and measures the following weights:

Weight, (lbs)

45.6     49.5

47.7     46.7

47.6     48.8

50.5     48.6

50.2     51.5

46.9     50.2

47.8     49.9

49.3     49.8

53.1     49.3

49.5     50.1

To determine whether the bags are indeed being underfilled by the machinery, the manager must conduct a test of mean with a significance level α = 0.05.

In a minimum of 175 words, respond to the following:

• State appropriate null (Ho) and alternative (H1) hypotheses.
• What is the critical value if we work with a significant level α = 0.05?
• What is the decision rule?
• Calculate the test statistic.
• Are the bags indeed being underfilled?
• Should machinery be recalibrated?

4. Suppose that we want to test the null hypothesis that the mean of a normal population with    σ² =1. Ho: μ = 10 vs Ha: μ > 10.   Determine the minimum sample size needed to test with β(11) = 0.06.

A factory that produces screws sells its products in packets of 100. A packet is considered defect if more than 10 screws (out of the 100) are defect. To test whether a packet is defective, 5 screws are picked at random and checked. If at most two of the five are defect, we say that the packet is not defective. Take Ho: the number of defect screws in a given packet is 10 and Ha : the number of defect screws is more than 10.

a. What is the probability for a type I error?

b. Given that the number of defective is 20. What is the probability for a type II error?

Is it true that the Sample means are less variable than individual observations as n→∞ ? Explain

Given the Data set: 8.5, 8.7, 8.9, 8.2, 8.3, 8.4, 8.5 – Use this set for parts a to d. This is to be considered as set2 for part c

1. [Find the Mean, Mode, Median, Range, Midrange and Standard Deviation for the Data Set
2. Determine if the following data set has an outlier that can be disregarded
3. Using the given data set#2 from the given data and set #1 being (?⃐ = 8.7 , S = 0.47 and N = 7) determine if the two data sets are statistically the same or different using an 90% confidence interval.
4. Find the range for the sample mean value with 80% confidence interval. Make sure µ is isolated