Statistics and Probability Answers

1.1 Define what we mean by a variable, and explain the difference between a quantitative variable and a qualitative (categorical) variable.

Hello - have I calculated the following correctly? Comments appreciated

Using a normal dice, rolled 5 times, the probability of rolling 2 sixes would be 1.61%

i.e 1/6 x 1/6 x 5/6 x 5/6 x 5/6 =125/7776

Using a normal dice, rolled 5 times, the probability of not rolling a six at all would be 40.19%

i.e 5/6 x 5/6 x 5/6 x 5/6 x 5/6 = 3125/7776

A study was conducted to determine whether an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child. A sample of 77 newborns whose mothers smoked during pregnancy has mean bone mineral content x-bar1 = 0.098 g/cm and standard deviation s1 = 0.026 g/cm; a sample of 161 infants whose mothers did not smoke has mean x-bar2 = 0.095 g/cm and standard deviation s2 = 0.025 g/cm. Assume that the underlying population variances are equal.

a. Are the two samples paired or independent?
b. State the null and alternative hypotheses of the two-sided test.
c. Conduct the test at the 0.05 level of significance. What do you conclude?

Question 7
Flaws in a carpet tend to occur randomly and independently at a rate of one every 200 square feet. What is the probability that a carpet that is 8 feet by 10 feet contains no flaws?

Question 6
The number of students who seek assistance with their statistics assignments is Poisson distributed with a mean of two per day.
a. What is the probability that no students seek assistance tomorrow?
b. Find the probability that 10 students seek assistance in a week.

Question 1
A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place 4 balls (marked A, B, C and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five multiple-choice questions on the exam. What is the probability that she will get
a. Five questions correct
b. At least four questions correct
c. No questions correct
d. No more than two questions correct

Question 2
A student majoring in accounting is trying to decide on the number of firms to which he should apply. Given his work experience and grades, he can expect to receive a job offer from 70% of the firms to which he applies. The student decides to apply to only four firms. What is the probability that he receives no job offers?

Heights of fathers and sons are given in centimeters.
Height of father
150
152
155
157
160
161
164
166
Height of son
154
156
158
159
160
162
161
164
Find the line of regression and calculate the expected average height of the son when the height of the father is 154cm.

Use the sign test to see if there is a difference between the number of days until collection of an account receivable before and after a new collection policy. Use the 0.05 significance level.

The Bayley Scales of Infant Development yield scores on two indices--the Psychomotor Development Index (PDI) and the Mental Development Index (MDI)--which can be use to assess a child's level of functioning in each of these areas at approximately one year of age. Among normal healthy infants, both indices have a mean value of 100. As part of a study assessing the development and neurologic status of children who have undergone reparative heart surgery during the first three months of life, the Bayley Scales were administered to a sample of one-year-old infants with congenital heart disease. The data contained in the data set heart. PDI scores are saved under the variable name pdi while MDI scores are saved under mdi. Use the treatment=1 group
a. At the 0.05 level of significance, test the null hypothesis that the mean PDI score for children born with congenital heart disease who undergo reparative heart surgery during the first three months of life is equal to 100, the mean score for healthy children. Use a two-sided test. What is the p-value? What do you conclude?

1. In a sample of 49 adolescents who served as the subjects in an immunologic study, one variable of interest was the diameter of a skin test reaction to an allergen. The sample mean and standard deviation were 21 and 11 mm erythema, respectively.
a. Use the Z or t-distribution? Why?
b. One-sided or two-sided test? Why?
c. Can it be concluded from these data that the population mean is less than 24 mm erythema?