Among a random group of 36 students, the average time spent daily on telephone calls was found to
be 20 minutes. Assuming that the amount of time spent daily on telephone calls by a student is a
random variable with distribution N(µ; 25), calculate the confidence interval for the mean duration,
assuming a confidence level of 0.88. How many students should be interrogated, in order to obtain a
confidence interval for the mean of length not exceeding 2, with a confidence level of 0.99?

The results of the test given to students are assume to be normally distributed with a mean of 57 and a standard deviation of 10. The passing score for the exam is 30.  Answer in figure only.

a) If a student is randomly selected, what is the probability that he or she passed the exam? Answer in 4 decimal places. Answer in percentage in in 2 decimal places.

b) A score of 75 or greater is needed to obtain an A on the exam. What percentage of the students received an A? Answer in 2 decimal places.

The scores on the final of a math class last semester had a median of 28 out of 40, with the highest
score of 39 and a lowest score of 6. Suppose that the curve had a normal distribution. Suppose
I took a simple random sample of 3 students from last semester and found their scores on the
final to be 15, 30, and 36. We wish to test the hypothesis that the average of all the students in
the adjunct was the lower than the average of the entire class.

1. In each of the following pairs, which situation (1) or (2) would pose the largest problems regarding adverse selection?

a. (1) A policy covering accidents for all children attending YMCA camps or (2) A policy covering accidents for college students traveling abroad

b. (1) Basic medical services insurance package offered to students entering college or (2) Basic medical services package offered to professors seeking early retirement

Five university students were given an English achievement test before and after receiving instruction in basic grammar. Their scores are shown below: Student Before After A 20 18 B 18 22 C 17 15 D 16 17 E 12 9

Should we conclude that future students would show higher scores after instruction? Use the .05 significance level. Use hypothesis testing.

This is a sampling distribution question in intro statistics.

During the last week of the semester, students at a certain college spend on the average 4.2 hours using the school's computer terminals with a standard deviation of 1.8 hours. For a random sample of 36 students at that college, find the probabilities that the average time spent using the computer terminals during the last week for the semester is

a) at least 4.8 hours

b) between 4.1 and 4.5 hours

Please show your work.

Include null and alternate hypothesis, a p-value, and a conclusion PRIVATE about the null hypothesis

A student claimed that the average grade in the night sections of Statistics was higher than the day sections. She used a sample of 35 students from night sections and found they had a mean of 78 with a standard deviation of 8. A sample of 32 day students had a mean of 75 with a standard deviation of 6. Is the student's hypothesis supported? (use α = .01)

A survey of 200 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. Suppose that based on the​ survey, 80 of the 200 students responded​ "yes."

​a) What is the value of the sample proportion ModifyingAbove p with caret​?

​b) What is the standard error of the sample​ proportion?

​c) Construct an approximate 95​% confidence interval for the true proportion p by taking plus or minus 2 SEs from the sample proportion.

Becoming more interested in what students do with their free time, a researcher collects several different samples of students and also notes the gender of the student. The results are below. Test to see whether or not activity is independent of gender at an alpha level of .01.

You would like to see whether providing extra time to students on their test allows for them to achieve a higher grade. In the past, the average mark on this test is 68 percent. You select 25 students from your current class, who were given extra time on the test and see their average grade was 72 minutes (St Dev = 8).

What is the appropriate hypothesis test? Why this is the correct test? What is the effect size?