In a school sports day, there are 110 students taking part in 3 events i.e. athletic, netball, and soccer. Some of them are also supporters. Overall 43 of them are girls. 40 students take part in athletic. There are 25 girls taking part in netball, and 5 play netball and athletic. As for boys, only 30 boys play soccer, and only 15 take part in athletic. Meanwhile, 20 students act as supporters. The number of boys who play soccer only is 6 times more than girls who take part in netball and athletic. Note that the events only girls play netball and only boys play soccer are mutually exclusive.

a. Illustrate the events. Write the proper symbol for each event.

b. If one student is selected, find the probability of:

i. student who play soccer and an athletic. (1 mark)

ii. student who play netball but not an athletic.
(1 mark)

iii. student who only take part in athletic.  

iv. student who take part in netball given that she is not an athletic, or the student play soccer.     

A Year 13 Statistics student was given an assignment where she had to design and conduct an experiment and analyse the data collected.

She decided to investigate whether being told that a quiz was easy or hard influenced the results of the quiz. All the students in a Year 9 class were given the same quiz after having been randomly allocated to one of three groups: Group 1 were told that it was a hard quiz, Group 2 were told it was an easy quiz and Group 3 were told nothing about the quiz. None of the students were told what the experiment was about.

She then carried out a randomisation test to compare the mean quiz marks for the three groups.

Which one of the following statements is false?

The response is the quiz mark.

There were 3 treatments; being told the quiz was easy, told it was hard or told nothing at all.

It was not possible to blind the students because they knew that they had been given a quiz.

The experiment used a completely randomised design.

The group that were told nothing about the quiz could act as the Control group.

Are teacher evaluations independent of grades? After the midterm, a random sample of 284 students were asked to evaluate teacher performance. The students were also asked to supply their midterm grade in the course being evaluated. In this study, only students with a passing grade were included in the summary table. Use a 5% level of significance to test the claim that teacher evaluations are independent of midterm grades.

Midterm Grade

(A) State the null and alternate hypotheses.

(B) Identify the appropriate sampling distribution: Chi-square test of independence, Chi-square goodness of fit, or Chi-square for testing or estimating σ² or σ.

(C) What is the value of the sample test statistic?

(D) Find or estimate the P-value.

(E) Based on your answers for parts (a) through (d), will you reject or fail to reject the null hypothesis?

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μμ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500500 .

In answering the questions, use zz‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 495495 and 505505 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score ¯xx¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 495495 and 505505 ? (Enter your answer rounded to four decimal places.)

probability:

In a school sports day, there are 110 students taking part in 3 events i.e. athletic, netball, and soccer. Some of them are also supporters. Overall 43 of them are girls. 40 students take part in athletic. There are 25 girls taking part in netball, and 5 play netball and athletic. As for boys, only 30 boys play soccer, and only 15 take part in athletic. Meanwhile, 20 students act as supporters. The number of boys who play soccer only is 6 times more than girls who take part in netball and athletic. Note that the events only girls play netball and only boys play soccer are mutually exclusive.

1. Illustrate the events. Write the proper symbol for each event.                                            
2. If one student is selected, find the probability of

1. student who play soccer and an athletic.                                                                      (1 mark)

2. student who play netball but not an athletic.                                                            (1 mark)

3. student who only take part in athletic.                                                                       

4. student who take part in netball given that she is not an athletic, or the student play soccer.                                                                                                                           

Tomorrow’s highest temperature can be lower than, higher than or the same as today’s highest temperature. After evaluating all the relevant information available, a weather forecaster has determined that the probability that tomorrow’s highest temperature will be higher than today’s is determined to be 65%. This is an example of using which of the following probability approach?

Select one:

A. Priori probability

B. Empirical probability

C. Subjective probability

D. Conditional probability

Because of the outbreak of the coronavirus, students of UM are allowed to opt for Pass/Fail grade for courses they enroll in the second semester of 2019/2020. An instructor of ISOM2002 believes that there will be more than 35% of the students in the course choosing this option. A random sample of 40 students of ISOM2002 reveals that 16 of them prefer to take the Pass/Fail option. At 5% level of significance, what would be the rejection rule if we want to test the instructor’s belief?

Select one:

A. Reject H₀ if t_STAT < –1.6849.

B. Reject H₀ if Z_STAT < –1.645.

C. Reject H₀ if Z_STAT > +1.645.

D. Reject H₀ if t_STAT > +1.6849.

A business school claims that students who complete a 3-month typing course can type a mean of more than 1200 words an hour. A random sample of 25 students who completed this course typed a mean of 1163 words an hour, with a sample standard deviation of 87 words. Assume that typing speeds for all students who complete this course have an approximately normal distribution. (a) Using the critical value method and a significance level of 1%, is there evidence to support the business school’s claim? (b) What would a Type II error be in this case?

A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 70% of the offspring resulting from this cross will have red flowers. To test this, 80 seeds from this cross were collected and germinated and 46 plants had red petals. (a) Is there sufficient evidence at the 0.02 significance level to indicate the proportion of the hybrid plants with red petals differs from 70%? Use the P-value method in your test. (b) What would a Type I error be in this case?

A researcher at the Annenberg School of Communication is interested in studying the use of smartphones among young adults. She wants to know the average amount of time that college students in the United States hold a smartphone in their hand each day. The researcher obtains data for one day from a random sample of 25 college students (who own smartphones). She installs an app that registers whenever the smartphone is being held and the screen is on. The sample mean is 230 minutes, with a standard deviation of 11 minutes.

What is the 99% confidence interval for average daily time a smartphone is used among college students?

What is the lower bound of the confidence interval?   

What is the upper bound of the confidence interval?

What decision should the researcher make about the null hypothesis? Be sure to explain your answer (e.g., what numbers provide the basis for this decision?).

Would our decision about the null hypothesis have been different if the researcher had initially hypothesized that women spend more time talking on their phones than men?

Explain all parts/information necessary to answer this question.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495 .

In answering the questions, use z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490 and 500 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 36 students. What is the standard deviation of the sampling distribution of their average score ¯x ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490 and 500 ? (Enter your answer rounded to four decimal places.)

probability:

You want to estimate the difference between the average grades on a certain math exam before the students take the associated math class and after they take the associated math class. You take the random samples of 5 students who have taken the class and 5 students who have not taken the class. You get the following results:

A) Determine the population(s) and parameter(s) being discussed.

B) Determine which tool will help us find what we need (one sample z test, one sample t test, two sample t test, one sample z interval, one sample t interval, two sample t interval).

C) Check if the conditions for this tool hold.

D) Whether or not the conditions hold, use the tool you choose in part B. Use C=95% for all confidence intervals and alpha=5% for all significance tests.

* Be sure that all methods end with a sentence describing the results *