## Statistics Final Exam Review With Answers

Follow Easel Activity Included This resource includes a ready-to-use interactive activity students can complete on any device. Easel by TpT is free to use! Learn more. Included are six different versions, each including 60 well chosen representative

#### Stat 1222: Introduction To Statistics Final Exams

Practice Test 3 8. You draw a sample of size 30 from a normally distributed population with a standard deviation of four. What is the standard error of the sample mean in this scenario, rounded to two decimal places? What is the distribution of the sample mean? Round to two decimal places 7. Suppose the sample size in this study had been 50, rather than Round your answer to two decimal places.

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#### Final Reviews

Comparing graphs of the standard normal distribution z-distribution and a t-distribution with 15 degrees of freedom df , how do they differ? Comparing graphs of the standard normal distribution z-distribution and a t-distribution with 15 degrees of freedom df , how are they similar? Use the following information to answer the next five exercises. Body temperature is known to be distributed normally among healthy adults.

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## Twenty Final Exam Questions

My mantra of ask good questions applies to exams as well as in-class learning activities. This week I present and discuss twenty multiple-choice questions that I have used on final exams. All of these questions are conceptual in nature. They require no calculations, they do not refer to actual studies, and they do not make use of real data. I certainly do not intend these questions to comprise a complete exam I strongly recommend asking many free-response questions based on real data and genuine studies as well.

At the end of this post I provide a link to a file containing these twenty questions, in case that facilitates using them with your students. Correct answers are discussed throughout and also reported at the end.

I like to think that this question assesses some basic level of understanding, but frankly Im not sure. Do students ever say that a standard deviation and a p-value can sometimes be negative? Not often, but yes. Do I question my career choice when I read those responses? Not often, but yes.

I sometimes ask an open-ended version of this question where I ask students to provide a counter-example if their answer is no.

I started asking this question after I noticed that some of my students believe that conducting a randomized experiment *always* justifies drawing a cause-and-effect conclusion, regardless of how the data turn out! The good news is that very few students give answer A. The bad news is that more than a few give answer C.

## Practice Test 1 Solutions

#### 1.1: Definitions of Statistics, Probability, and Key Terms

**2**. c

#### 1.2: Data, Sampling, and Variation in Data and Sampling

**4**. d

**5**. c

**6**. Answers will vary. * * *

Sample Answer: Any solution in which you use data from the entire population is acceptable. For instance, a professor might calculate the average exam score for her class: because the scores of all members of the class were used in the calculation, the average is a parameter.

**7**. b

**11**. 0.55

**12**. Answers will vary. * * *

Sample Answer: One possibility is to obtain the class roster and assign each student a number from 1 to 200. Then use a random number generator or table of random number to generate 30 numbers between 1 and 200, and select the students matching the random numbers. It would also be acceptable to write each students name on a card, shuffle them in a box, and draw 30 names at random.

**13**. One possibility would be to obtain a roster of students enrolled in the college, including the class standing for each student. Then you would draw a proportionate random sample from within each class .

**15**. a

**21**. 13.2

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## Practice Test 2 Solutions

#### Probability Distribution Function for a Discrete Random Variable

**1**. The domain of *X* = {English, Mathematics,.], i.e., a list of all the majors offered at the university, plus undeclared.

**2**. The domain of *Y* = , i.e., the integers from 0 to the upper limit of classes allowed by the university.

**3**. The domain of *Z* = any amount of money from 0 upwards.

**4**. Because they can take any value within their domain, and their value for any particular case is not known until the survey is completed.

**5**. No, because the domain of *Z* includes only positive numbers . Possibly the value 7 is a data entry error, or a special code to indicated that the student did not answer the question.

**6**. The probabilities must sum to 1.0, and the probabilities of each event must be between 0 and 1, inclusive.

**7**. Let *X* = the number of books checked out by a patron.

**8**. *P* = 0.10 + 0.05 = 0.15

**9**. *P* = 1 0.20 = 0.80

**10**. *P* = 1 0.05 = 0.95

**11**. The probabilities would sum to 1.10, and the total probability in a distribution must always equal 1.0.

#### 4.4: Geometric Distribution

**29**. *T T T T H*

**30**. The domain of *X* = . Because you are drawing with replacement, there is no upper bound to the number of draws that may be necessary.

**32**. *X* ~ *G*

3.16

**38**. *X* ~ *P*

## Questions On Statistics With Answers

**1. Give any two examples of collecting data from day-to-day life.**

Solution:

A. Increase in population of our country in the last two decades.

B. Number of tables and chairs in a classroom

Presentation of Data: After the collection of data, when we represent them in the form of table or chart or any other means, which help us to have a quick glance over the data, it is said to be its presentation. It also means a rearrangement of raw data in a particular order. |

**2. If marks obtained by students in a class test is given as per below:**

**55 36 95 73 60 42 25 78 75 62**

**Then arrange the marks from lowest to highest.**

Solution: We need to arrange the marks obtained by each student in ascending order:

25 36 42 55 60 62 73 75 78 95

**3. Check the following frequency distribution table, consisting of weights of 38 students of a class:**

Weights |

** What is class-interval for classes 31 35?**

** How many students are there in the range of 41-45 kgs?**

Solution:

Class interval = Upper class limit lower class limit

= 35-31

For the 41-45 range, there are 14 students.

**4. A family with a monthly income of ` 20,000 had planned the following expenditures per month under various heads:**

Heads |

Now with these class marks we can plot the frequency polygon as shown below.

Solution:

Mean = /5 = 35000/5 = 7000

So, the mean salary is Rs. 7000 per month

To obtain the median, let us arrange the salaries in ascending order:

5000, 5000, 5000, 5000, 15000

Median = /2 = /2 = 6/2 = 3rd observation

Median = Rs. 5000/-

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