Standard deviation

PLEASE SHOW WORK…..

1.                  True or False. Justify for full credit.

(a)    The standard deviation of a data set cannot be negative.

(b)   If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.2.

(c)    The mean is always equal to the median for a normal distribution.

(d)   A 95% confidence interval is wider than a 98% confidence interval of the same parameter.

(e)    In a two-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Student’s t-distribution with P(T < 1.5) = 0.98, then we fail to reject the null hypothesis at 0.05 level of significance .

2.                  Identify which of these types of sampling is used: cluster, convenience, simple random, systematic, or stratified. Justify for full credit.

(a)                A STAT 200 professor wants to estimate the study hours of his students. He teaches two sections, and plans on randomly selecting 10 students from the first section and 15 students from the second section.

(b)               A STAT 200 student is interested in the number of credit cards owned by college students. She surveyed all of her classmates to collect sample data.

(c)                The quality control department of a semiconductor manufacturing company tests every 100th product from the assembly line.

(d)               On the day of the last presidential election, UMUC News Club organized an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left those polling stations.

3.                  The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. (Show all work. Just the answer, without supporting work, will receive no credit.)

Checkout Time (in minutes)

Frequency

Relative Frequency

1.0 - 1.9

3

2.0 - 2.9

12

3.0 - 3.9

0.20

4.0 - 4.9

3

5.0 -5.9

Total

25

(a)               Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places.

(b)               What percentage of the checkout times was at least 4 minutes?

(c)                Does this distribution have positive skew or negative skew? Why?

4.                  A box contains 3 marbles, 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box, then replacing it in the box and drawing a second marble from the box. (Show all work. Just the answer, without supporting work, will receive no credit.)

(a)                List all outcomes in the sample space.

(b)               What is the probability that at least one marble is red? (Express the answer in simplest fraction form)

5.                  The five-number summary below shows the grade distribution of two STAT 200 quizzes for a sample of 500 students.

Minimum

Q1

Median

Q3

Maximum

Quiz 1

15

30

55

85

100

Quiz 2

20

35

50

90

100

For each question, give your answer as one of the following: (i) Quiz 1; (ii) Quiz 2; (iii) Both quizzes have the same value requested; (iv) It is impossible to tell using only the given information. Then explain your answer in each case.

(a)                Which quiz has less interquartile range in grade distribution?

(b)               Which quiz has the greater percentage of students with grades 90 and over?

(c)                Which quiz has a greater percentage of students with grades less than 50?

6.                  There are 1000 students in a high school. Among the 1000 students, 800 students have a laptop, and 300 students have a tablet. 250 students have both devices. Let L be the event that a randomly selected student has a laptop, and T be the event that a randomly selected student has a tablet. Show all work. Just the answer, without supporting work, will receive no credit.

(a)                Provide a written description of the event L OR T.

(b)               What is the probability of event L OR T?

7.                Consider rolling two fair dice. Let A be the event that the two dice land on different numbers, and B be the event that the first one lands on 6.

(a)                What is the probability that the first one lands on 6 given that the two dice land on different numbers? Show all work. Just the answer, without supporting work, will receive no credit.

(b)               Are event A and event B independent? Explain.

8.                  There are 8 books in the “Statistics is Fun” series. (Show all work. Just the answer, without supporting work, will receive no credit).

(a)               How many different ways can Mimi arrange the 8 books in her book shelf?

(b)               Mimi plans on bringing two of the eight books with her in a road trip. How many different ways can the two books be selected?