Statistics and Probability Answers

We are interested to know whether test animals respond to temperature by moving
toward a favoured temperature. Animals were placed in a temperature gradient marked
in units from zero (the starting point) in the middle of the gradient to positive at the
warm end and negative at the cold end. The mean position along the gradient was found
to be -1.352 units, the standard deviation was 12.267 units and n=500 individuals. Is
there a significant tendency to aggregate at either the cold or warm end of the gradient?
Start by setting up a null hypothesis in terms of the mean position along the gradient =
0. (This question is graded out of 12 marks)

A population has a mean of 100 and standards of deviation of 20 suppose a simple random sample of size 100 is selected and is used to estimate u . What is the probability that the sample proportion mean will be within +_ 2 of the population mean?

N red cards and 2N black cards (all distinct) are shuffled together to form a single deck, and then split into half. What is the probability that each half will contain N red and N black cards

An explosion in a factory manufacturing explosive can occur because of 1. leakage of electricity, 2. defects in machinary, 3. carelessness of worker or 4. sabotage. The probability that (a) there is a leakage of electricity is 0.20 (b) the machinery is defective is 0.30 (c) the workers are careless is 0.40 (d) there is sabotage is 0.10

comcertain motor oil is packed in tins holding 5 litres each. The filling machine can maintain this but with a S.D. of 0.15 litre. Two samples of 36 tins each are taken from the production line. If the sample means are 5.20 and 4.95 litres respectively, can we be 99% sure that the sample have come from a population of 5 litres?

Economists at the Wilson Company are interested in developing a production function for fertilizer plants. They collected data in 15 different plants that produce fertilizer ( see in the following table).

QUESTION
1. Estimate the Cobb-Douglas production function Q= αLβ₁Kβ₂, where Q = output; L = labor input; K =capital input and α, β₁, and β₂ are the parameters to be estimated
2. Test whether the coefficients of capital and labor are statistically significant.
3. Determine the percentage of the variation in output that is “explained” by the regression equation
4. Determine the labor and capital estimated parameters and give an economic interpretation of each value.
5. Determine whether this production function exhibits increasing, decreasing, or constant returns to scale. (Ignore the issue of statistical significance.)

Suppose that 100 items are drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a non-normal probability distribution with mean = 8 ounces and standard deviation = 3 ounces. Consider the sampling distribution of the sample mean of the weights . a. Can you describe the sampling distribution of the sample mean? Explain why. b. Find the mean and variance of the sample mean? c. Find the probability that the mean weight is greater than 8 ounces. d. Find the probability that the mean weight is less than 6 ounces. e. Find the probability that the mean weight is between 7 ounces and 9 ounces
Expert's answer

Sharon runs a day care center. Of the last 10 children to enroll at the day care center, 4 of them have been preschoolers. What is the experimental probability that the next child to enroll will be a preschooler?

By doing electric circuit with resistors in series and parallel-measuring potential difference and current. Make inference about the observations recorded in the table ,graph ,drawing , photographs .make some conclusions.what did you find out?do your result support your hypothesis?what did you learn from this investigation?

1. A writer has prepared to submit six articles for publication. The probability of an article
being accepted is 0.20. Assuming independence, find the probability that the writer will
have
i. Exactly one article accepted
ii. At least two articles accepted
iii. No more than three articles accepted
iv. At most two articles accepted