A grading scale is set up for 1000 students’ test scores. It is assumed that the scores are normally distributed with a mean score of 80 and a standard deviation of 10:

a)    What proportion of students will have scores between 40 and 85?

b)    If 60 is the lowest passing score, what proportion of students pass the test?

c)    What score would a student have to score to be in the 68^th percentile?

d)    What score would a student have to make to be in the top 20% of the class?

e) If 60 is the lowest passing score, estimate how many students pass the test?

A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 157 students using Method 1 produces a testing average of 65.9. A sample of 129 students using Method 2 produces a testing average of 80. Assume the standard deviation is known to be 12.47 for Method 1 and 12.84 for Method 2. Determine the 95% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2.

Step 1 of 2:

Find the critical value that should be used in constructing the confidence interval.

Some statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.72. Suppose that we randomly pick 25 daytime statistics students.

1. Give the distribution of X.

2. Give the distribution of

X.bar

(Round your standard deviation to three decimal places.)

3. Find the probability that an individual had between $0.68 and $1.00. (Round your answer to four decimal places.)

4. Find the probability that the average of the 25 students was between $0.68 and $1.00. (Round your answer to four decimal places.)

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 257 students was x¯¯¯x¯ = 140 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σσ = 65 minutes in the population of all first-year students at this university.

Use the survey result to give a 95% confidence interval for the mean study time of all first-year students.

please explain your process. Thank you

A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. For convenience we use the labels CS for computer science majors, EO for engineering and other science majors, and O for other majors. The explanatory variables included several high school grade summaries coded as 10 = A, 9 = A-, etc. Here are the mean high school mathematics grades for these students. Major Gender CS EO O Males 8.68 8.35 7.65 Females 9.11 9.36 8.04 Describe the main effects and interaction using appropriate graphs and calculations.

Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a​ professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The

200 students in group 1 had a mean score of 21.8

with a standard deviation of 3.5, while the 200 students in group 2 had a mean score of 19.9

with a standard deviation of 4.6.

Complete parts ​(a) and ​(b) below.

​(a) Determine the 95​% confidence interval for the difference in​ scores, μ1−μ2. Interpret the interval.

(b) What does this say about​ priming?

Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a​ professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The

200 students in group 1 had a mean score of 21.8

with a standard deviation of 3.5, while the 200 students in group 2 had a mean score of 19.9

with a standard deviation of 4.6.

Complete parts ​(a) and ​(b) below.

​(a) Determine the 95​% confidence interval for the difference in​ scores, μ1−μ2. Interpret the interval.

(b) What does this say about​ priming?

1. Within a school district, students were randomly assigned to one of two Math teachers - Mrs. Smith and Mrs. Jones. After the assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25 students. At the end of the year, each class took the same standardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10; and Mrs. Jones' students had an average test score of 85, with a standard deviation of 15. Assume the variances are equal. At the significance level 0.10, can we conclude that Mrs. Jones is a more effective teacher than Mrs. Smith?

     a). Calculate the test statistic. (R code and R result).

     b). Find the p-value (R code and R result).

     c). Make your decision.

Suppose a student organization at the University of Illinois collected data for a study involving class sizes from different departments. A random sample of 11 classes in the business department had an average size of 38.1 students with a sample standard deviation of 10.6 students. A random sample of 12 classes in the engineering department had an average size of 32.6 students with a sample standard deviation of 13.2 students

a. Perform a hypothesis test using a = 0.05 to deter-mine if the average class size differs between these departments. Assume the population variances for the number of students per class are not equal.
b. Approximate the p-value using Table 5 in Appen-dix A and interpret the results.
c. Determine the precise p-value using Excel.

d. What assumptions need to be made in order to perform this procedure?