A pollster would like to survey 500 students to determine the percentage that would vote for Ben Carson. If the pollster surveyed 500 students who worked directly with Carson will the results be meaningful to depict the thinking of the entire US population of students? Answer yes or no with explanation.

Why was Marilyn Vos Savant's calculation of having breast cancer given a positive mammogram test flawed?

A. Hubble telescope sees a dime sized view of the universe which represents an accurate sample

B. Jhon Hickley is insane

C. Fibonacciseries appears eveerywhere in nature

D.Women who get mammograms have a higher probability of breast cancer than the random American and Marilyn used the random American probabillity in her calculation.

A school district developed an after-school math tutoring program for high school students. To assess the effectiveness of the program, struggling students were randomly selected into treatment and control groups. A pre-test was given to both groups before the start of the program. A post-test assessing the same skills was given after the end of the program. The study team determined the effectiveness of the program by comparing the average change in pre- and post-test scores between the two groups. During the course of the program, some students in both the treatment and control groups either dropped out of school or they moved away with their families. Could this attrition potentially distort the estimated effectiveness of the tutoring program? Defend your answer.

1. Answer the following by SHOWING ALL YOUR WORK

A) Suppose there was a class of 200 students with a mean class average of 63%. I then select from this class all students on the honor roll, which amounts to 53 students. Would you expect their average to be the same? Why or why not?

B) According to the label on a drink bottle, the bottle should contain 500 mL of product. Currently, the filling machine is set to a mean volume of 502 mL and a standard deviation of 1.5 mL. If too many cans are under-filled, they risk losing customers, but if the can surpasses 505 mL of fill, there will be spillover when the bottle is capped, wasting product. Does the company need to recalibrate the machine?

1. A questionnaire about study habits was given to a random sample of students taking a
large introductory statistics class. Students were asked if they studied most nights in a week: yes or
no. The results are that the sample proportion of students who answered “yes” (?̂) was 0.4.

Consider the same scenario as in Problem 1.
a) Calculate a confidence interval for sample size n = 1000, ?̂= 0.4, and the following confidence
levels: 80%, 90%, and 99%. You can use your confidence interval from Problem 1 with n = 1000
for 95% so you don’t have to recalculate it.
b) Answer the question: As the confidence level increases from 80% to 99% what happens to the
width of the confidence level?

In an​ experiment, college students were given either four quarters or a​ $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts​ (a) through​ (c) below. Purchased Gum Kept the Money Students Given Four Quarters 30 12 Students Given a​ $1 Bill 14 26 a. Find the probability of randomly selecting a student who spent the​ money, given that the student was given four quarters. The probability is 0.714. ​(Round to three decimal places as​ needed.) b. Find the probability of randomly selecting a student who kept the​ money, given that the student was given four quarters. The probability is nothing. ​(Round to three decimal places as​ needed.)

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.

(a)

What is the probability of completing the exam in one hour or less? (Round your answer to four decimal places.)

(b)

What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? (Round your answer to four decimal places.)

(c)

Assume that the class has 80 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time? (Round your answer up to the nearest integer.)

students

1. Some colleges have pushed back the starting time of morning classes because students were not getting enough sleep. A random sample of 46 college students had an average of 6.54 hours of sleep with a standard deviation is 1.90 hours. Compute and interpret a 98% confidence interval for the population mean amount of sleep that college students get per night. Also determine the critical values and calculate the margin of error.

2.The Travel Channel wants to conduct a survey of adults who take weekend vacations to Las Vegas. If the channel wants to be 97% confident that the sample percentage is in error by no more than 1.75 percentage points, how many adults must be surveyed?

1. US News publishes annual statistics based on the performance and demographic data reported for major universities. Suppose this year, US News releases its publication and finds that only 6% of students at a particular university consider themselves African-American. The response at the University was outrage, and a local student group conducted a comprehensive survey in order to correct the publication that they believe was flawed. Suppose that, out of a sample of 3,496 students, the university found that 487 identified as African-American.

Conduct a formal test to determine if the proportion of students identifying as African-Americans differs significantly from the proportion published in US News. Use an α=0.05. Be sure to include each of the four steps of hypothesis testing. Do not use excel.

. (Education) A researcher would like to know whether there is a consistent, predictable relationship between verbal skills and math skills for high school students. A sample of 300 students is obtained and each student is given a standardized English test and a standardized math test. Based on the test results, students are classified as high, medium, or low for verbal skills and for math skills. The results are summarized in the following frequency distribution:

verbal skills

Math skills

Based on these results, can the researcher conclude that there is a significant relationship between verbal skills and math skills at the 10% level of significance?

For the following questions, indicate what kind of analysis you would perform and identify the hypothesis.

2. Consider the gain in weight of 99 female rats between 28 and 84 days after birth. 40 were fit on a high protein diet and 59 on a low diet (Expect a higher weight for high protein diet). Suppose we find the standard deviation between the two groups are equivalent.

3. In fall 2017, students in the 9:30 am section (45 students) of Biological statistics class had an average height of 66.6 inches, while the average height in the 11:30 am section (55 students) was 64.6 inches. Are the average heights of the two sections significantly different?