Statistics and Probability Answers

a) In one sample of observations, the sum of the squares of the observations of the sample values from sample mean was 120 and in the other sample of 12 observations it was 314. Test whether the difference is significant at 5% level of significance

Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. Evaluate the data below. Do you think that their cholesterol levels were significantly lowered? (Show all your work i.e. Ho and Ha, p-value, conclusion in words)

b) A researcher reports that the average salary of assistant professors is more than £42,000. A sample of 30 assistant professors has a mean salary of £43,260 at a = 0.05, test the claim that assistant professors earn more than £42,000 per year. The standard deviation of the population is £ 5,230.

The Mental Development Index (MDI) for infant development is a standardized measure used in longitudinal

follow-up of high risk infants. The MDI scores are known to be normally distributed with mean 100 and variance
256. For a study of infants, a random sample of size 400 is selected.

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® and Off®), 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 x, 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.

Study of sea turtles.research shows the shell Lengths have a distribution with a mean of 50cm and a standard dev of 10cm.in the study n76 turtles where captured the mean length for the sample was 55.5cm.how likely is it to observe a sample mean of 55.5cm or larger?

Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 2.83 (p. 65). Research shows that the curved carapace (shell) lengths of these turtles has a distribution with mean μ = 50 cm and standard deviation σ = 10 cm. In the study, n = 76 green sea turtles were captured from the lagoon; the mean shell length for the sample was = 55.5 cm. How likely is it to observe a sample mean of 55.5 cm or larger?

Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 2.83 (p. 65). Researchers discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with mean 55.7 centimeters and standard deviation 11.5 centimeters.
a. The minimum and maximum size limits for captured turtles in the legal marine turtle fishery are 40 cm and 60 cm, respectively. How likely are you to capture a green sea turtle that is considered illegal?
b. What maximum limit, L, should be set so that only 10% of the turtles captured have shell lengths greater than L?

let x have a uniform distribution on the interval [A,B]. Compute V(X)

A table has drawers. Drawer 1 contains two red and five black biros, draw 2 contains four red and three black biros and drawer 3 contains on red and six black biros. A drawer is chosen at random and a biro is chosen from the drawer. Find the probability that the biro chosen is from drawer 1 if the chosen biro is black