# Statistics Problem Set: Confidence Level

1) For the following sequence: 2,4,7,3,9,4,7,11 find the range, mode, median, mean, IQR, standard deviation, variance and whether it is normally distributed (with explanation)

2) An investor wants to assess at confidence level of 98% if a medicament can improve the marks of students. He notices that for the following daily dozes: 2,2.5,3,4.5,7 mg, the improvement over the students that studied the same but took no mental boosters were of: 3,4,4.6,6, 8.5 percent. At a confidence interval of 99%, what results would you expect for the students who take a daily dose of 6.5 mg? show full calculations.

3) A T 95 tank weighs 75 tons. A businessman wants to buy a couple of thousand tanks for hunting expedition in Texas. He will buy only if the tanks are really as specified and refuse to buy them if they statistically they weigh less. He takes a sample of 8 tanks and finds their average weight at 74.7 tons with a standard deviation of 0.3 tons. He wants to use a significance level of 2%. What will be his best course of action. Show all the work and justify your answer.

4) A car has a gas mileage of 500 miles per gallon of gasoline, with a standard deviation of 10 miles per gallon. What would be the gas mileage of the top 40% of such cars? What would be the mileage range for 70% of the cars? What %of cars will have a mileage of 530 miles per gallon of less?

5) The probability that a student answers a multiple question correctly is 27%, in an exam with 6 questions. What would be the probability the students answers correctly at random: no question, all questions, 6 questions, less than two and more than 4 questions? Answer individually all these questions, show all the work and explain your logic.

6) Mr. G. just won the jackpot with one ticket. He chose correctly 6 numbers out of 52 numbers and 2 stars our out of 12 stars. What was his probability of winning when he bought the ticket? Show full work and explain your answer.

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#### Solution Preview

1. Please refer to the excel attachment for the calculations.

2. Please refer to the excel attachment for the calculations.

3. Null Hypothesis: The mean weight is greater than or equal to 75 tons.

H0: u >= 75

Alternate Hypothesis: The mean weight is less than 75 tons.

H1: u < 75

Let us ...

#### Solution Summary

The expert finds the range, mode, median, mean, IQR, standard deviation and variance. The mental boosters are provided.

Statistics Problem Set: Intervals

5.2. What is the confidence level of each of the following confidence intervals for the mean? (see attached).

5.20. The "Raid" test kitchen. According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers for S.C. Johnson & Son, Inc. (manufacturers of Raid), 5,000 roaches (the expected number in a roach-infested house) were released in the Raid test kitchen. One week later, the kitchen was fumigated, and 16,298 dead roaches were counted, a gain of 11,298% roaches for the 1-week period. Assume that none of the original roaches died during the 1-week period and that the standard deviation of the number of roaches produced per roach in a 1-week period is 1.5. Use the number of roaches produced by the sample of 5,000 roaches to find a 95% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house.

5.4. A random sample of 90 observations produced a mean of 25.9 and a standard deviation of 2.7.

a. Find an approximate 95% confidence interval for the population mean.

b. Find an approximate 90% confidence interval for the mean.

c. Find an approximate 99% confidence interval for the mean.

5.10. Latex allergy in health care workers. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Symptoms of a latex allergy include conjunctivitis, hand eczema, nasal congestion, skin rash, and shortness of breath. Each in a sample of 46 hospital employees who were diagnosed with latex allergy based on a skin-prick test reported their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are mean =19.3 and standard deviation = 11.9.

a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy.

b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy.

c. Give a practical interpretation of the interval, part b.

d. Give the conditions required for the interval, part b, to be valid.