Mathematics , Statistics-Intro To Statistics

1. Matching answers to questions (10%)

 

Questions:What is the sampling design?

1. ________ The data of customer preferences were collected by asking the first 111 people who entered the store.
2. ________ A survey study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in a community. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed.
3. ________ A study about career goal of the University of Maryland undergraduate students was conducted for which every student registered as of May 30, 2018 has an equal probability of being selected and interviewed.
4. ________ A study about career goal of the University of Maryland undergraduate students was conducted as follows: students are divided into subgroups according to their majors, and then 5% of students from each of subgroups are randomly selected for interview.
5. ________ UMUC conducted a study of student opinions about Stat-200 course by randomly selecting 5 out of 30 on-going Stat-200 classes, and then interviewed all the students in these 5 selected classes.

 

Answer:

1. Clustering
2. Convenience
3. Random sampling
4. systematic
5. Stratified

 

2.True or false (20%)

 

a.______P(A and B)= P(A) +P(B)

b.______If events A and B are independent, then P(A and B) = P(A) x P(B)

c.______If a null hypothesis H₀ is not significant, then the alternative H₁ must be true.

d.______If A and B are mutually exclusive, thenP(A or B) = P(A)+P(B)

e.______ If a null hypothesis is not rejected by a 2-tailed test, then the null hypothesis cannot be rejected under a one-tailed test

1. _______The mean, median, and mode of a normal distribution are equal.
2. _______ The area under a probability distribution curve (e.g., a normal distribution) is always equal to 1.0.
3. ________ Normal distributions are defined by two parameters, the mean and the standard deviation.
4. ________ 68% of the area of a normal distribution is within one standard deviation of the mean.
5. _______ If a null hypothesis is not rejected by a 2-tailed test, then the null hypothesis cannot be rejected under a 1- tailed test.

 

 

3. Traffic engineers observed the traffic flow at I-200 has mean speed of 70 miles, with a SD=10 miles. The posted speed limit is 65 miles, what is the proportion of cars exceeding the limit of 65 miles. (10%)

(hint: )

 

4. Given the following box plot: (15%)

 

Figure 2.41

 

1. Which quarter has the smallest spread of data? What is that spread?

 

1. Which quarter has the largest spread of data? What is that spread?

 

1. Find the interquartile range (IQR).

 

 

 

5. You flip a coin three times. What is the probability of getting heads on at least one flip? (15%)

 

 

 

6. Imagine a sample of 15 subjects with a mean score of 10 and standard error of 3. What’s the 95% confidence interval of the mean? (hint: use t-distribution)(15%)

 

7. Roll two fair dice. Each die has six faces. (15%)
   1. List the sample space.(hint: The sample space has 36 elements, consisting pairs of numbers such as (1,1), and (1,2).)

 

1. Let A be the event that either a three or four is rolled first, followed by an even number.

List all elements of the event A and find P(A).

 

1. Let B be the event that the sum of the two rolls is at most seven.

List all elements of the event B, and find P(B).