Students in a different statistics class were asked to report the age of their mothers when they were born. Here are the summary statistics:

Sample size: 28     sample mean: 29.643 years         sample stDev: 4.564 years

1. Calculate the standard error of this sample mean.
2. Determine and interpret a 90% confidence interval for the mother’s mean age (at student’s birth) in the population of all students at the college.
3. How would a 99% confidence interval compare to the 90% confidence interval in terms of its midpoint and half-width?
4. Would you expect 90% of the ages in the sample to be in the 90% confidence interval? Explain why or why not.

The average American sees 15 movies per year. Amy believes that UCI students are different from the average American regarding movies. She gets a sample of four UCI students and asks them how many movies they see per year. They answer 2, 14, 2, 10. Do a t-test to see if Amy’s belief is true. Please calculate the t-statistic for this data. State the critical value, and come to a conclusion about Amy’s belief. Let α = .05. Make it a two-tailed test. Assume that it is okay to do a t-test.

In a large introductory statistics lecture​ hall, the professor reports that 53​% of the students enrolled have never taken a calculus​ course, 28​% have taken only one semester of​ calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group. What is the probability that of your other two​ groupmates,

​a) neither has studied​ calculus?

​b) both have studied at least one semester of​ calculus?

​c) at least one has had more than one semester of​ calculus?

At a certain university 12% of students are left hand users. Suppose that a random sample of 8 students were admitted in 2015 is selected.

(a) What is the probability that none of them will be a left hand user?

(b) What is the probability that 5 of them are left hand users?

(c) What is the probability that at least 7 of them are left hand user?

(d) What is the probability that at most 7 of them are left hand user?

(e) What is the probability that between 4 and 6 (inclusive) of them are left hand user?

(f) What is the expected value and standard deviation of number of users with left hand?

School administrators wondered whether class size and grade achievement (in percent) were related. A random sample of classes revealed the following data:  

No. Students (x) 15 10 8 20 18 6

Avg. grade (%) (y) 85 90 82 80 84 92

Use a significance level of .05 to test the claim that the two variables (no. students and avg grade) are linearly related.

Based on your analysis, what is the best predicted avg grade for a class size of 12 ? Round your answer to one decimal place (i.e. one digit to the right of the decimal place)

In a group of students, there are 2 out of 18 that are left-handed.

a. Assuming a low-informative prior probability distribution, find the posterior distribution of left-handed students in the population. Summarize your results with an estimation of the mean, median, mode, and a 95% credible interval. Plot your posterior probability distribution.

b. According to the literature, 5 to 20% of people are left-handed. Take this information into account in your prior probability and calculate a new posterior probability distribution. Summarize your results with an estimation of the mean, median, mode, and a 95% credible interval. Plot your posterior probability distribution.

The average math SAT score is 523 with a standard deviation of 115. A particular high school claims that its students have unusually high math SAT scores. A random sample of

60 students from this school was​ selected, and the mean math SAT score was 540. Is the high school justified in its​ claim? Explain.

(Yes.No) because the​ z-score () is (unusual,not unusual) since it (lies, does not lie)

within the range of a usual​ event, namely within (1 standard deviation,2 standard deviations, 3 standard deviations) of the mean of the sample means.

​(Round to two decimal places as​ needed.)

Put It in Writing Activity: Imagine that you have just been hired as the principal of a high school where students’ attendance and test performance has been poor and the dropout rate has been high. At a meeting with your teachers, you explain that the principles of classical and operant conditioning could be used to improve the situation.

Write a page describing how these principles could be used to increase students’ class attendance, study skills, and test performance.

Be sure to label all the concepts and principles you use (such as “conditioned stimulus,” “positive reinforcement,” “conditioned response,” “discriminative conditioned stimulus,” “shaping,” and the like)

Let's assume our class represents a normal population with a known mean of 90 and population standard deviation 2. There are 100 students in the class.

a. Construct the 95% confidence interval for the population mean.

b. Interpret what this means.

c. A few students have come in. Now we cannot assume normality and we don't know the population standard deviation. Let the sample mean = 90 and sample standard deviation = 3. Let's make the sample size 20. We can assume alpha to be .05. Construct the 95% confidence interval assuming this new information.

Each student arrives in office hours one by one, independently of each other, at a steady rate. On average, three students come to a two-hour office hour time block. Let S be the number of students to arrive in a two-hour office hour time block.

What is the distribution of S? What is its parameter?

Group of answer choices

S ∼ Geo(1/3)

S∼Pois(3)

S∼Bin(2,1/3)

S-Pois(1.5)

What is the probability that S = 4?

What is the probability that S ≤ 2?

What is the variance of S?

What is the expected value of S?