One way to evaluate the effectiveness of a course instructor is to examine the scores achieved by his or her students in an examination at the end of the course. Obviously, the mean score is of interest. However, the variance also contains useful information - some teachers have a style that works very well with more able students but is unsuccessful with less able or poorly motivated students. A professor sets a standard examination at the end of each semester for all sections of a course. The variance of the scores on this test is typically very close to 300. A new instructor has a class of thirty students, whose test scores had a sample quasi-variance of 480. Regarding these students’ test scores as a random sample from a normal population:

(a) At a 5% significance level, test against a two-sided alternative the null hypothesis that the population variance of their scores is 300.

(b) Based on your answer to 4a, decide if a 95% confidence interval for the population variance would include the value of 300.

(c) Calculate the power of the test.

(d) Draw the power function from 4c in R.

(e) Looking at the graph from 4d, what is the probability of Type II error for σ 2 = 500 (roughly)?

The superintendent of a large school district speculated that high school students involved in extracurricular activities had a lower mean number of absences per year than high school students not in extracurricular activities. She generated a random sample of students from each group and recorded the number of absences each student had in the most recent school year. The data are listed below. Test the superintendent’s claim at the α=.01 significance level. [To receive full credit, your response should be sure to state your hypotheses, check the relevant requirement(s), find a test value, find a critical value or p-value (either is OK), make your decision, and state your conclusion.]

Students in EC Activities: 4 1 2 0 5 6 2 1 0 3 0 1 1 4 8 6 9 2 0 4 2 10 5 6 1

Students not in EC Activities: 5 7 0 9 4 3 12 8 4 2 0 5 5 4 9 14 6 10 9 6 3

7) A researcher suspects that there is a direct relationship between hand-eye coordination and academic success in math. A sample of n = 16 students who have demonstrated above average performance on a second-grade math test is selected. These students are given a standardized hand-eye coordination task where the average score for this group is μ = 55. The 16 students in the sample produced a mean of 61 with SS of 540.

     a) Are the data sufficient to conclude that the high math achievement students have hand-eye

          coordination scores that are significantly different from the general population? Use a two-tailed

          test with α = .01.

     b) Are the data sufficient to conclude that the high math achievement students have hand-eye

          coordination scores that are significantly better than the general population? Use a one-tailed  

          test with α = .01.

8) A newspaper article reported that the typical American family spent an average of μ = $81 for Halloween candy and costumes last year. A sample of n =16 families this year produced a mean of $85 with SS = 6000. Do these data indicate a significant change in holiday spending? Use a two tailed test with α = .05.

A student conducts a simple random sample of students from her high school and finds that 21 out of 100 students in her sample regularly walk to school. Give a point estimate for the proportion of all students at her high school who regularly walk to school. For each combination of sample size and sample proportion, find the approximate margin of error for the 95% confidence level. (Round the answers to three decimal places.) In a sample of 16 students, 15 were right-handed. Can we construct a 95% confidence interval for the proportion of all students who are right-handed? A study reported that 49% of Internet users have searched for information about themselves online. The 49% figure was based on a random sample of Internet users. Suppose that the sample size was n = 400. In a randomly selected sample of 400 registered voters in a community, 260 individuals say that they plan to vote for Candidate Y in the upcoming election. A certain set of plants were constantly dying in the dry environment that was provided. The plants were moved to a more humid environment where life would improve.

Fremont High School has 2100 students. One of the statistics teachers at the school is interested in whether an intervention program based on self-management improves attendance. They randomly choose 80 students and randomly assign half of them to either an experimental condition (self- management class) or a control condition (distractor class on popular culture). At the end of the semester, they measure the number of days missed for each student. The teacher expects that the students in the self-management class will be absent for fewer days than the control group.

1) What is the population in this experiment?

2) What is the sample in this experiment?

3) What is the response variable in this experiment?

4) If the teacher calculates the average number of absences for the group of 80 students, then that average would be a______. A. Parameter B. Statistic

5) If the teacher calculates the average number of absences from all the 2100 students, then that average would be a_______. A. Parameter B. Statistic

6) The teacher records the number of absences for each student. This record is her______.

Number of absences is a______.

A. data; continuous B. data; discrete

7) Number of absences is a______.

A. Ratio B. Interval C. Nominal D. Ordinal

Suppose that the IQs of university​ A's students can be described by a normal model with mean 140 and standard deviation 8 points. Also suppose that IQs of students from university B can be described by a normal model with mean 120 and standard deviation 11. ​

a) Select a student at random from university A. Find the probability that the​ student's IQ is at least 130 points. The probability is nothing. ​(Round to three decimal places as​ needed.) ​

b) Select a student at random from each school. Find the probability that the university A​ student's IQ is at least 10 points higher than the university B​ student's IQ. The probability is nothing. ​(Round to three decimal places as​ needed.)

​c) Select 3 university B students at random. Find the probability that this​ group's average IQ is at least 125 points. The probability is nothing. ​(Round to three decimal places as​ needed.) ​

d) Also select 3 university A students at random.​ What's the probability that their average IQ is at least 10 points higher than the average for the 3 university B​ students? The probability is nothing. ​(Round to three decimal places as​ needed.)

More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye.

A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.72 hours and SD(X) = 1.16 hours.

- Find the probability that the hours of sleep per night for a random sample of 4 college students has a mean x between 6.8 and 6.91.

- Find the probability that the hours of sleep per night for a random sample of 16 college students has a mean x between 6.8 and 6.91. (use 4 decimal places in your answer)

- Find the probability that the hours of sleep per night for a random sample of 25 college students has a mean x between 6.8 and 6.91.(use 4 decimal places in your answer)

-The Central Limit Theorem was needed to answer questions 1, 2, and 3 above.

True

False    

Use the table below to calculate the answers to the questions that follow it. Be sure to write how you are calculating your answer. You must include the numbers from the table when showing your work. The following table shows a sample of CSI students who are interested attending the “CSI has talent” show and whether they live on Staten Island. Results of a survey follow

A) What proportion of students are interested in attending the show?

B) What proportion of SI residents are interested in attending show? What proportion of non-SI residents are interested in attending the show? Which type of student is more likely to be interested in attending the show?

C) Assume that the proportion of all CSI students who are interested in attending the show is 0.6, what is the sampling distribution of the proportion of students who are interested in attending the show based on a sample size of 360 students?

D) How likely is it that would get a sample proportion less than what we obtained in part a?

Use the following for the next 4 questions: A nationwide survey of college students was conducted and found that students spend two hours per class hour studying. A professor at your school wants to determine whether the time students spend at your school is significantly different from the two hours. A random sample of fifteen statistics students is carried out and the findings indicate an average of 2.1 hours with a standard deviation of 0.24 hours. Using the 0.10 level of significance, can we conclude that the time students spend studying at your school is different from 2 hours?

H0: U= 2 Min

H1: U=/ 2 Min

1) What Kind of test is this?

One-tail (left tail)

Two-tail

One-tail (right tail)

2) What is the critical value? State the positive one.

3)  What is the value of the test statistic? Round to three decimal places.

4) What is your decision regarding the null hypothesis?

e) What is your conclusion?

1) There is not a difference in amount of time spent studying at your school

2) There is a difference in the amount of time spent studying at your school

A) The total distances covered by GIMPA Undergraduate students to and from their work
places every month is normally distributed with a mean 105 km and variance of 225 km2
.
a. What percentage of the population of students covered less than 90 km in a month in other
words what is the probability of finding a student who covers less than 90 km in a month?
(1 mark)
b. The percentage of students who cover above 140 km every month (1 mark)
c. The percentage of students who cover between 100 and 120 km every month (1 mark)
d. What is the least distance of the top 0.1 decile category of the distances covered by students
in a month? (2 mark)
B) A health clinic found that in a sample of 200 women, the mean and the standard deviation
of their masses are 85.5kg and 10.5kg, respectively. Also, 115 women were found to be over-
weight.
a. Find point estimates of the mean mass and proportion of over-weight in women population.
(1 mark)
b. Construct a 95% confidence interval for population mean mass. ( 2 marks)
c. Construct a 95% confidence for proportion of over-weight in women population.