A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters.

a) The students are interested in using the width of the beans to predict the height. Calculate the slope of the regression equation.

b) Write the equation of the best-fit line that can be used to predict bean heights. Use x to represent width and y to represent height.    

c) What fraction of the variability in bean heights can be explained by the linear model of bean height vs width? Express your answer as a decimal.

d) If, instead, the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation.

e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width

A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters.

Mean width: 7.439 Stdev width: 0.88 Mean height: 13.625 Stdev height: 1.825 Correlation coefficient: 0.7963

a) The students are interested in using the width of the beans to predict the height. Calculate the slope of the regression equation. b) Write the equation of the best-fit line that can be used to predict bean heights. Use x to represent width and y to represent height. c) What fraction of the variability in bean heights can be explained by the linear model of bean height vs width? Express your answer as a decimal. d) If, instead, the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.

We have seen in lectures that if 50 people are chosen at random then there is a 97% chance that at least two of them share the same birthday. Use similar calculations to answer the questions below. Assume that an ANU student is equally likely to have any one of 000 ... 999 as the last three digits of their ID number.

(a) What is the percentage chance that in a working group of five students at least two have the same last digit of their ID?

(b) What is the percentage chance that from a course with an enrolment of 100 students at least two have the same last three digits of their ID?
NB: If your calculator cannot handle the large numbers involved, you could use WolframAlpha (www.wolframalpha.com) or some other on-line tool.

(c) By experimenting using WolframAlpha, or otherwise, find the minimum number N for which there is a better than even chance that from N randomly chosen students at least two have the same last three digits of their ID. As a start, try N = 40.

The figure below shows a frequency and​ relative-frequency distribution for the heights of female students attending a college. Records show that the mean height of these students is

64.564.5

inches and that the standard deviation is

1.81.8

inches. Use the given information to complete parts​ (a) through​ (c).

a. The area under the normal curve with parameters

mu equals 64.5μ=64.5

and

sigma equals 1.8σ=1.8

that lies to the left of

6464

is

0.39470.3947.

Use this information to estimate the percent of female students who are shorter than

6464

inches.

nothing​%

​(Type an integer or a decimal. Do not​ round.)

Table C (below) shows the schedules for marginal social cost, marginal private benefit, and marginal social benefit of a university education for each student.

1. Assuming a competitive free market for private university education (i.e. with no government involvement in university education), how many students are likely to enrol? 1 mark.
2. What is likely to be the university fee per student? 1 mark.
3. What is the socially efficient enrollment level? 1 mark.
4. What is the marginal external benefit per student at the socially efficient enrollment level? 1 mark.
5. If the government subsidises universities so that thesocially efficient number of students will enrol, what is the amount paid by taxpayers? 1 mark.

Table C

Many educational institutions award three levels of Latin honors often based on GPA. These are laude (with high praise), magna laude (with great praise), and summa laude (with the highest praise). Requirements vary from school to school. Suppose the GPAs at State College are normally distributed with a mean of 2.9 and standard deviation of 0.43.

(a) Suppose State College awards the top 2% of students (based on GPA) with the summa laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.
GPA or higher

(b) Suppose State College awards the top 10% of students (based on GPA) with the magna laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.
GPA or higher

(c) Suppose State College awards the top 20% of students (based on GPA) with the laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.
GPA or higher

Bianca is conducting a study on high school​ students' perceptions of the importance of​ e-mail as a communication method. She is particularly interested in whether​ first-year high school students have different​ attitudes/beliefs about​ e-mail than do their senior peers. She gives a​ 10-question survey to a sample of 12 students. A completed survey for you to view is located in course materials.

A. Will you analyze single​ items, summed​ scores, or difference​ scores?

B.  One participant​ (Senior #5) has inadvertently marked her answer for Item 7 in the row for Item​ 6, resulting in two answers for Item 6. What should you do to account for the extra​ data? Would it be preferable to delete her data entirely from the​ dataset, or would you average the two scores together and assign that as the score for Item​ 6. Explain your answer.

C. Based on the information you​ have, discuss the limitations for this particular study.

Consider the approximately normal population of heights of male college students with mean μ = 72 inches and standard deviation of σ = 8.2 inches. A random sample of 12 heights is obtained.

(a) Describe the distribution of x, height of male college students.

skewed right, approximately normal, skewed left

(b) Find the proportion of male college students whose height is greater than 74 inches. (Give your answer correct to four decimal places.)

(c) Describe the distribution of x, the mean of samples of size 12.

skewed right, approximately normal, skewed left, chi-square

(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)


(e) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)


(f) Find P(x > 68). (Give your answer correct to four decimal places.)


(g) Find P(x < 68). (Give your answer correct to four decimal places.)

23.) Assume that a sample is used to estimate a population proportion p. Find  the margin of error E given that the confidence level is 99%, the sample size is 1216, of which 32% are successes.  Round your answer to four decimal places.

24.)Find the margin of error E. In a random sample of 212 college students, 105 had part-time jobs. Find the margin of error E for the 95% confidence interval used to estimate the population proportion. Round your answer to four decimal places.

25.)Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 97, x = 46; 98% confidence

26.) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

When 319 college students are randomly selected and surveyed, it is found that 120 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.