The accompanying data represent the pulse rates​ (beats per​ minute) of nine students. Treat the nine students as a population. Compute the​ z-scores for all the students. Compute the mean and standard deviation of these​ z-scores.

Student   Pulse
Student 1   77
Student 2   60
Student 3   60
Student 4   80
Student 5   72
Student 6   80
Student 7   80
Student 8   68
Student 9   73

Compute the mean of these​ z-scores.

The mean of the​ z-scores is

​(Round to the nearest tenth as​ needed.)

Compute the standard deviation of these​ z-scores.

The standard deviation of the​ z-scores is
(Round to the nearest tenth as​ needed.)

The ages of a group of 141 randomly selected adult females have a standard deviation of 18.9 years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let σ=18.9years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students? Assume that we want

95​% confidence that the sample mean is within​ one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population?

Assume that a study was done on students who were completing their last semester of college and had already secured offers of employment. That study showed that the students' utility could be modeled as u(HW, PAY, EXAMS) = 500PAY - 5HW - 3EXAMS, where PAY is weekly starting pay after graduation, in thousands of dollars; HW is hours of homework per week from all classes for the semester; and EXAMS is the number of exams per semester. Based on the observed utility function, how much weekly pay would students be willing to give up to reduce homework by 6.00 hours per week? Round your answer to two decimal places.

3. Suppose someone claims that the average GPA in a University is at least 2.85.
But in a class with 23 students, we find the average GPA in that class is 2.78,
with standard deviation 0.35. Can we reject the claim at significance level 0.10
?

4. Is the random machine really random? Suppose to check the random
machine, we let the machine to produce 10,000 digit numbers (0, 1, ..., 9). We
find the number of 1’s is 1080. Can we say with α=0.05, that the machine is
not really random?

5. Suppose someone claims that the average GPA for all students in this
university is at least 3.00. To test this hypothesis, we set H_0: μ=3.0, H_1:
μ<3.0. Suppose a professor asks you to check a random sample of 36 students,
and tells you that if the sample mean is less than 2.95, then, reject the claim.
For this decision making rule, find α, the probability for making Type I error
(assume the standard deviation of GPA for all students is 0.4).

4. A teacher believes that whatever he says in class has no effect on his students. Just as he's about to quit his profession, a statistician enters the room and suggests that the teacher design a study to test his assumption. The study will look at whether providing in-class feedback on homework assignments enhances classroom performance. The teacher wants to know whether providing feedback before or after returning the assignments is most useful. He's also interested in the most effective means of presenting the feedback: verbal presentation, written handout, or a summary on overheads. Ultimately, he'd like to identify the best approach for increasing test scores of the students. There are 12 classes available in the school for the experiment. Design an experiment that helps answer these questions. Be sure to identify the factors, the levels of the factors, the treatment groups, and the response variable. Comment on how the students will be assigned to the different treatment groups. Is it possible to use simple random assignment of all students? As much as possible, use diagrams instead of words to summarize your experimental design.

A study examined parental influence on the decisions of teenagers from a certain large region to smoke. A randomly selected group of​ students, from the​ region, who had never smoked were questioned about their​ parents' attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found​ that, among the 256 students who indicated that their parents disapproved of kids​ smoking, 72 had become established smokers. Among the 30 students who initially said their parents were lenient about​ smoking,11 became smokers. Do these data provide strong evidence that parental attitude influences​ teenagers' decisions about​ smoking?

a) What kind of design did the researchers use?

b) Write the appropriate hypothesis

c) Are the assumptions and conditions satisfied?

d) Test the hypothesis and state the conclusion z score and p value

Reject or do not reject

Explain the p value

What type of error was committed

Create a 99% CI

Interpret interval

The accompanying data represent the pulse rates (beats per minute) of nine students. Treat the nine students as a population. Compute the z-scores for all the students. Compute the mean and standard deviation of these z-scores.

STUDENT          PULSE

student 1               77

student 2               61

student 3               60

student 4               80

student 5               73

student 6               80

student 7               80

student 8               68

student 9               73

Compute the z-scores for all the students. complete the table. (round to the nearest hundredth as needed)

STUDENT      Z-SCORE    

student 1         ___

student 2     ___

student 3         ___

student 4        ____

student 5.      ____

student 6.      ____

student 7.       ____

student 8.       _____

student 9.      _____

Now, compute the mean of these z-scores. (round to the nearest tenth as needed.)

The mean of the z-scores is ___.

Now, compute the standard deviation of these z-scores. (round to the nearest tenth as needed.)

The standard deviation of the z-scores is ____.

A student survey was completed by 446 students in introductory statistics courses at a large university in the fall of 2003. Students were asked to pick their favorite color from black, blue, green, orange, pink, purple, red, yellow.

(a) If colors were equally popular, what proportion of students would choose each color? (Round your answer to three decimal places.)

(b) We might well suspect that the color yellow will be less popular than others. Using software to access the survey data, report the sample proportion who preferred the color yellow. (Round your answer to two decimal places.)

(c) Is the proportion preferring yellow in fact lower than the proportion you calculated in (a)?

(d) Use software to produce a 95% confidence interval for the proportion of all students who would choose yellow.
(e) How does your confidence interval relate to the proportion you calculated in (a)?

it is strictly below that proportion it contains that proportion     it is strictly above that proportion

The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans.

(a) Construct a 99% confidence interval for estimating the true proportion of all university students who have student loans (2 marks)

(b) Provide an interpretation of the confidence interval in part (a). (1mark)

(c) Conduct an appropriate hypothesis test, at the 1% level of significance to test the claim that more than 30% of all university students have student loans.

1. Provide the hypothesis statement

2. Calculate the test statistic value

3. Determine the probability value

Note: if you need to use symbols , please use

• "u" for population mean "μ",

• Ho and Ha for  for the null and alternate hypothesis,

• "Y-hat" for "ŷ", "alpha" for α

Please provide your answers to the above questions by typing your answers using simple text. You need not show the work in detail.