The time needed for college students to complete a certain paper-and-pencil maze follows a normal distribution with a mean of 30 seconds and a standard deviation of 2 seconds. You wish to see if the mean time μ is changed by vigorous exercise, so you have a group of 20 college students exercise vigorously for 30 minutes and then complete the maze. It takes them an average of x¯=27.2 seconds to complete the maze. Use this information to test the hypotheses H0:μ=30 Ha:μ≠30 Conduct a test using a significance level of α=0.01. (a) The test statistic (b) The positive critical value, z =

By some estimates, thirty-­‐percent (30%) of all students in Groningen go on ski vacation each year. Out of a random sample of 300 students, what is the approximate probability that more than 100 of them went to ski this year? (Use the normal approximation)

And:

Oscar is getting married in Brazil where it rains only 1% of the time. Unfortunately, the weather expert has predicted rain for tomorrow. On a given day, there is a 9% chance that the weather expert predicts rain. 90% of the time that the weather expert has forecasted rain, it does in fact rain. What is the probability that it will rain on the day of Oscar´s wedding?

Suppose you are interested in knowing the average cholesterol level of all women between the ages of 21 and 30 who live in College Station. Everyone in a class (100 students) takes a random sample of 50 females in the College Station area between the ages of 21 and 30. Each student calculates the average cholesterol in their sample. Jenna is one of the students in this class and she makes a histogram of the 50 cholesterol levels in her sample. What kind of distribution would be displayed in Jenna's histogram?

7.38 Teaching descriptive statistics. A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. (a) What are the hypotheses for evaluating if the average test scores are different for the different teaching methods? (b) What are the degrees of freedom associated with the F-test for evaluating these hypotheses? (c) Suppose the p-value for this test is 0.0168. What is the conclusion?

1. For each of the following, state whether the quantity described is a parameter or a statistic, and give the correct notation.

1.   Correlation between height and arm-span (distance from fingertip to fingertip when arms are extended to the sides) for all players on the Chicago Bulls basketball team, using data from all players currently on the team

2. Average gas price in Minnesota, based on prices at randomly selected gas stations throughout the state.

3. Proportion of students at a university that are part-time, based on data on all students enrolled at the university.

4. Correlation between age and heart rate for patients admitted to an Intensive Care Unit, based on a sample of 200 patients.

4. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution. (Source: http://www.ets.org/.) Suppose a random sample of 10 students took the test, and their scores are given below. 152, 126, 146, 149, 152, 164, 139, 134, 145, 136 a) Test the claim that the mean verbal reasoning score is different from 150 at the α = 0.10 level of significance. Do the step process to show work.

b) It has been claimed that the standard deviation of the GRE scores is 8.8. Is there sufficient evidence to conclude that the standard deviation

Part 1) When 500 Rowen College students were surveyed, 110 said they own their car. Find a point estimate for p, the population proportion of students who own their cars. Round your answer to 3 decimal places.

Part 2) We intend to estimate the average driving time of Rowen College commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 11 minutes. We want our 99% confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size.

Part 1) When 500 Rowen College students were surveyed, 110 said they own their car. Find a point estimate for p, the population proportion of students who own their cars. Round your answer to 3 decimal places.

Part 2) We intend to estimate the average driving time of Rowen College commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 11 minutes. We want our 99% confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size.

Which of the following variables have a binomial distribution?

1) Find the largest value of x that satisfies:
log5(x2)−log5(x+5)=8

2) Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model
f(t)=90−7log(t+1),    0≤t≤24
where t is the time in months. Round answers to at least 1 decimal point.

A) What is the average score on the original exam?

B) What was the average score after 6 months?

C) What was the average score after 18 months?