Statistics and Probability Answers

(3.2.7) Listed below are the top 10 annual salaries​ (in millions of​ dollars) of TV personalities. Find the​ range, variance, and standard deviation for the sample data. Given that these are the top 10​ salaries, do we know anything about the variation of salaries of TV personalities in​ general?
42,40,38,30,20,16,13,10,9.6,8.3

The brain volumes ​(cm3​) of 20 brains have a mean of 1172.9 cm3 and a standard deviation of 129.3 cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such​ data, would a brain volume of 1471.5 cm3 be significantly​ high?

suppose the previous example is stated a little bit differently. Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is more effective for women than for men. To test this claim, they choose a a simple random sample of 100 women and 200 men from a population of 100,000 volunteers.

At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we conclude that the drug is more effective for women than for men? Use a 0.01 level of significance

3. A paint-store chain produces and sells latex and semigloss paint. Based on long-range sales among these two paints, the probability that a customer will purchase latex paint is 0.75. Of those that purchase latex paint, 60% also purchase rollers. But only 30% of semigloss paint buyers purchase rollers. A randomly selected buyer purchases a roller and a can of paint. What is the probability that the paint is latex?

(a) What is the probability that a customer will purchase a roller? (Give answer in decimal form in thousandths place. Ex. 0.031)
(b) What is the probability that the paint is semigloss? (Give answer in simplified fraction form. Ex. 31/51)
(c) What is the probability that the paint is latex? (Give answer in simplified fraction form. Ex. 31/51)

2. A regional telephone company operates three identical relay stations at different locations. During a one-year period, the number of malfunctions reported by each stations and the causes are shown below. Suppose that a malfunction was reported and it was found to be caused by other human errors.

(a) What is the probability that the malfunction is caused by human error? (Give answer in simplified fraction form. Ex. 31/51)
(b) What is the probability that the human error was caused by station C? (Give answer in simplified fraction form. Ex. 31/51)
(c) What is the probability that the human error was caused by station B? (Give answer in simplified fraction form. Ex. 31/51)
(d) After a year, it was observed that the 1 in 4 malfunctions by human error was caused by station B. Basing on last year's data and still considering human errors, what is the new probability that the station B caused the malfunction.

1. In a certain region of the country, it is known from past experience that the probability of selecting an adult over 40 years of age with cancer is 0.05. If the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of incorrectly diagnosing a person with cancer as having the disease is 0.06,

(a) what is the probability that an adult over 40 years of age is diagnosed as having cancer? (Give answer in decimal form in thousandths place. Ex. 0.031)
(b) What are the chances that a person has no cancer but is still diagnosed otherwise? (Give answer in percentage form. Please include percentage sign. Decimal must be in the thousandths place. Ex. 99.999%)

You want to impress your family and you are wondering if you could find a farm where you could be sure to get very big pumpkins, like 25 pounds on average. A friend shows you the 4 pumpkins she got at the SuperPumpkins Farm, and you are able to calculate that the mean weight of this sample of 4 pumpkins to be 27 pounds. To find out the true population mean weight at the SuperPumpkins Farm, you decide to build a 99% confidence interval with this sample data from your friend, assuming that the population standard deviation should be 6 pounds (i.e. typical for pumpkins, the same as the Huckleberry Farm). Based on this confidence interval you built, do you feel confident that the SuperPumpkins Farm will have very big pumpkin of around 25 pounds on average. round to 2 decimals, !

2. Suppose a researcher has a record on data set consisting of 300 readings on pressure (kg/cm2
)
exerted on a surface of a new metal alloy in order to study the hardness of the new alloy.
Demonstrate application of a scheme to transform the variables down the hierarchy of
measurement scales. At each level of the hierarchy, suggest a statistical analysis applicable on
the values of the variables measured using the corresponding scale.

If your critical value is
±
1.6 then you are running a:
two tailed test
left tailed test
unable to determine from this information
right tailed test