Last summer I collected data from my students and it turned out that their average height was 67” with standard deviation 4.0”. There were 58 students in class that day. I want to know if my students are, on average,taller than I am? I am 64” tall.

1. we are testing

2. H_0:

_3. H_a:

4. We will do a z-procedure because the sample size is large.

5. If the population mean __________ is indeed __________, then due to sampling variation alone __________ of all possible sample mean __________ are expected to be ________________________________________, when the samples consist of __________ ____________________ each.

5. The number of daily texts sent by Marymount students are normally distributed with a mean of 80 texts and a standard deviation of 50 texts.

(a) Find the probability that a randomly selected Marymount student sends more than 100 texts each day.

(b) Find the probability that 25 randomly selected Marymount students will have a mean number of daily texts sent that is greater than 50 texts.

(c) Suppose a parent wants their child in the bottom 25% of texters. Find the cut-off value for the number of texts below which 25% of MCU students lie.

if possible include graph

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full time college students who earn a bachelors degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.05 margin of error and use a confidence level of 99%.

A. Assume that nothing is known about the percentage to be estimated

N =

B. Assume prior studies have shown that about 35% of full time students earn bachelors degrees in four years or less

C. Does the added knowledge in part b have much of an effect on the sample size?

This problem involves normalizing a sample proportion.

6.    Past data has shown that 20% of all students graduating from XYZ University go on to do post-graduate work. A random sample of 700 students was taken frorn the university population.

1. Find the probability that the sample proportion of students going on to do postgraduate work is greater than 24%. (Hint: Note that 20% is the population proportion, and 24% is the sample proportion.)
2. State the numerical value of the standard error of the proportion.

This problem involves a test in which two independent populations are involved and the population standard deviations are known.

Suppose 56 out of 100 randomly selected students support the proposal that will
shorten the semester to 15 weeks.
A. What is the sample proportion of supporting the proposal?
B. Under what conditions can we use normal distribution to approximate the
distribution of sample proportion? Verify if these conditions hold.
C. Find a 95% confidence interval for the proportion of all students who support
the proposal.
D. Suppose no students are surveyed. What sample size does the investigator
need to have to achieve a margin of error of at most 3% with 95%
confidence. Suppose we do not have an estimate of population

Use RStudio. To test if a middle school class on geography is working, a pre- and post-test were given to students at the start and end of the semester. Assume that the scores were randomly selected from the two tests. Also, assume that that they are pairs of scores for ten students. Use the following data to test if the class improved students’ knowledge of geography. (hint: use “var.equal=TRUE” in your argument)

Scores

Pre-test:     77, 56, 64, 60, 57, 53, 72, 62, 65, 66

Post-test: 88, 74, 83, 68, 58, 50, 76, 64, 74, 60

A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.

Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.)
z =

1. Imagine that the psychology department wants to consult you on a project designed to measure how students’ expectations for the difficulty of Intro to Psychology class actually influences their final grade. The department randomly selects 50 Intro students at the beginning of the semester and asks them, “What grade do you expect to get in Intro to Psychology this semester?” Below are the numbers students reported for their expected grade.

Note: A = 4.0, B = 3.0, C = 2.0, D = 1.0, F = 0.0

Expected grades: 0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4

Using the data above, construct a simple frequency distribution, a relative frequency, cumulative frequency and a percentile

3. The Idaho State University athletics department conducted a research study to see how many students attended a women’s lacrosse game last season. There are 14,400 students attending Idaho State University, and the study showed that 400 of 1250 students sampled attended a women’s lacrosse game. What inferences can be made about student attendance at women’s lacrosse games?

(a) What is the estimated proportion for the population?

(b) Using the 95% level of confidence, what is the confidence interval?

(c) Using the 99% level of confidence, what is the confidence interval?

PLEASE SHOW ALL WORK

A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.

Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.)
z =