The heights of 13-year-old girls are normal distribution with mean 62.6 inches and a standard deviation of 7.2 inches. Erin is taller than 80% of the girls her age. How tall is Erin?

A researcher wishes to use students' IQ 's to predict their SAT. There is a correlation of 0.82 between SAT scores and IQ scores. The average SAT verbal score is 500, with a standard deviation of 100. The average IQ score is 100 with a standard deviation of 15.

Calculate the equation for the least-squares regression line

Before going to the market, a pregnancy test has been applied to a population of 10,000 women from which 300 were actually pregnant. Suppose this new product  returns a “yes” result 99.5 % of the cases in which the person was actually pregnant and 98% of the cases returns  a “no” result when the person was not pregnant.

Now that the test is in the market: what is the probability that a random user (a women) of the test is not pregnant if the test returns a “yes “ result? Draw  the appropriated probability tree

Constructing and Interpreting Confidence Intervals. In Exercises 13–16, use the given sample data and confidence level. In each case, (a) find the best point estimate of the population proportion p; (b) identify the value of the margin of error E; (c) construct the confidence interval; (d) write a statement that correctly interprets the confidence interval.

Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Construct a 95% confidence interval for the proportion of medical malpractice lawsuits that are dropped or dismissed.

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 45 and standard deviation σ = 11. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

Two transmitters send messages through bursts of radio signals to an antenna. During each time slot each transmitter sends a message with probability 1/2. Simultaneous transmissions result in loss of the messages. Let X be the number of time slots until the first message gets through.

(a) Describe the underlying sample space S of this random experiment and specify the probabilities of its elementary events.

(b) Show the mapping from S to the range of X.

(c) Find the probabilities for the various values of X. Now suppose that terminal 1 transmits with probability 1/2 in a given time slot, but terminal 2 transmits with probability p.

(d) Find the pmf for the number of transmissions X until a message gets through.

(e) Given a successful transmission, find the probability that terminal 2 transmitted.

if I have two lists:

A = {132.65, 327.86, 0.08, 1059.22, 5.29, 0.0, 454.04, 0.0, 193.67, 940.54}

B = {28.31, 0.0, 0.0, 6.71, 2336.61, 0.0, 90.17, 6.4, 244.29, 87.38}

I want to test if the variance of B is greater than A, how should I test it?

what is my Null and Alternative Hypothesis? what test should I run? and what is the result? do I reject my null and why?

A 7th grade science teacher was interested in knowing if his after-school tutoring sessions would boost grades for the students in his classes. The sample consisted of all the children in his 4th and 5th hour classes. The teacher gave a pre-test to each class. Then he held twice weekly sessions for 1 hour after school for four weeks. Students required permission from their parents/guardians in order to attend. Approximately 3/4 of the students for both hours attended. At the end of the 4th week, the teacher gave a post-test and measured the gains/losses in scores. He noted a significant increase in scores and attributed those gains to his tutoring sessions.

1. Identify at least two potential threats to the validity of his study and therefore to the results.

2. Discuss the threats - how might they affect the study results?

3. Propose a method for each threat to reduce/eradicate it.

Height: 62, 67, 62, 63, 67, 74, 63, 73, 63

Weight: 130, 140, 102, 140, 145, 157, 130, 190, 135

2. (CLO 1) Construct a confidence interval to estimate the mean height and the mean weight by completing the following:

a. Find the sample mean and the sample standard deviation of the height.

b. Find the sample mean and the sample standard deviation of the weight.

c. Construct and interpret a confidence interval to estimate the mean height.

d. Construct and interpret a confidence interval to estimate the mean weight.

3. (CLO 2) Test a claim that the mean height of people you know is not equal to 64 inches using the p-value method or the traditional method by completing the following:

a. State H0 and H1.

b. Find the p value or critical value(s).

c. Draw a conclusion in context of the situation.

4. (CLO 3) Create a scatterplot with the height on the x-axis and the weight on the y-axis. Find the correlation coefficient between the height and the weight. What does the correlation coefficient tell you about your data? Construct the equation of the regression line and use it to predict the weight of a person who is 68 inches tall.

5. Write a paragraph or two about what you have learned from this process. When you read, see, or hear a statistic in the future, what skills will you apply to know whether you can trust the result?

Find the value of z that would be used to test the difference between the proportions, given the following. (Use G - H. Give your answer correct to two decimal places.)

1. The following data is the survival time of a set of patients who had Glioblastoma (it is the time from detection until death): {5.28, 6.36, 9.72, 0.25, 5.52, 0.24, 76.8, 15.12, 11.52, 21.84, 2.76, 5.4, 15, 4.8, 1.08}.

Construct a Q-Q plot (normal probability plot) for the data

One card is selected from an ordinary deck of 52 cards. Find the conditional probabilities:

a) A spade given the card is black_____________

b) A spade given the card is red____________

c) A 4 given the card is not a picture card________________

d) A king given the card is a picture card________________

e) A king given the card is not a 2,3,4, or 5________________

Exercise 8.65. A child who gets into an elite preschool will have a lifetime earning potential given by a Poisson random variable with mean $3,310,000. If the child does not get into the preschool, her earning potential will be Poisson with mean $2,700,000. Let X = 1 if the child gets into the elite preschool, and zero otherwise, and assume that P(X = 1) = p.

(a) Find the covariance of X and the child’s lifetime earnings.

(b) Find the correlation of X and the child’s lifetime earnings.

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ.

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

Consider a random sample of size n = 41, with sample mean x = 45.0 and sample standard deviation s = 5.7.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(c) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(d) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.