A certain stat teacher believes that her students should do at least an average of 5 hours of homework in a week. She took a random sample of stat students this semester. Their sample mean amount of homework time was 3.6 hours with a standard deviation of 1.8 hours. The sample size was 32. Test the state teacher’s claim that her students do at least an average of 5 hours of homework in a week at the 1% level of significance. Show calculations. state hypotheses; include sketch; answer in context.

A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 20 who took the test each number of times. Number of time test was taken (x) 1 2 3 4 Number of students 7 6 4 3

What is the expected value of the number of tests taken?

What is the variance?

What is the standard deviation?

The percent of blue-eyed people in the US is estimated to be about 15%. A random sample of 20 Providence College students is taken.
a) Use the binomial distribution to find the probability that [Round to 4 decimal places .XXXX]
(i) None of the 20 students have blue eyes.
(ii) at most 5 have blue-eyes
(iii) 3 or more have blue-eyes
b )Find the expected number of students who would have blue-eyes in a random sample of 20.

9. You are interested in studying the average duration of time (in minutes) it takes Temple University students to drive to campus. The conventional wisdom is that on average it takes students 30 minutes to drive to campus. To examine this, you randomly sample n=15 students and record this information. From the sample, you compute a sample mean of 26 with a sample standard deviation of 6. Conduct a two-tailed hypothesis test with 95% confidence. Then, construct a 95% confidence interval to confirm your answer.

9. (19) A random sample of 64 UPW college students shows that the sample mean GPA is 2.82 with a standard deviation of 0.45.

(a) Construct a 90% Confidence Interval for the mean GPA of all UPW students.

(b) If we want to be 95% confident, and we want to control the maximum error of estimation to 0.1, how many more students should be added into the given sample?

(c) Would you conclude that the mean GPA in UPW is lower than 3 at 5% level of significance?

1) It is claimed that students use computer networks on average 5 hours a day in an educational institution consisting of 2500 students. The average duration of use of the computer alarur for 10 randomly selected students was 5.3 hours, and the standard deviation was 1.2. Create Type 1 error and Type 2 error scenarios for the situation above. In which case, Type 1 error, in which case Type 2 error would have been made, please explain on the given example

1. A survey of all students in a school showed that 3/7 have a dog, and 2/7 have a cat, and 1/7 have both a dog and a cat. If a student is selected at random, what is the probability of the student having OR a cat?

2. 40% of the students at a college live in the dorms. Of the students who live in the dorms, 10% are juniors. If a student from the college is picked at a random, what is the probability he or she is a junior who lives in the dorm?

Please explain and show steps.

a recent study in 2016 says 72% of students spend at least 5 hours on electronics per day. the sample has 100 observations and 75 out of 100 students stated that they spend at least 5 hours on electronics every day. formulate a hypothesis test that can be used to determine if the proportion of college students who spend at least five hours a day on electronics has increased. what is the z score and what is your conclusion at significance= 0.01? confirm using p value.

A health journal found that

56.2​%

of college students who lived in coed dormitories consumed alcohol weekly​ (compared with​ 26.5% who lived in​ single-sex dormitories). A random sample of 175

students who live in coed dormitories was selected. Complete part d below.

d. Identify the symmetric interval that includes 95​% of the sample proportions with a sample size of 175 if the true population proportion of students in coed dormitories who consume alcohol weekly is 56.2​%.

(%), (%)round to one decimal

Suppose 250 randomly selected students in a college are surveyed to determine if they own a tablet. Of the 250 surveyed, 98 reported owning a tablet.

a. explain whether normal model can be used in this situation

b. find the standard error.

c. Construct the 95% confidence interval and explain what it means in the context of the problem

d. based on the college database, the proportion of students that owns a tablet in this college is 36% What is the probability, that a sample of 250 random selected students, more than 100 owns a tablet?