1 – Assume that a class consisting of 40 students took an exam. 15 students got A, 20 got B, and 5 got C. If you randomly select three students without replacement, what is the chance that you get one student with grade A, one student with grade B, and one student with grade C?
2 – Assume that a class consisting of 40 students took an exam. 15 students got A, 20 got B, and 5 got C. If you randomly select three students without replacement, what is the chance that you get at least one student with grade C?
3 – Assume that you are designing a process to produce a special type of metal. Two factors are very important to produce the metal with an acceptable quality: Temperature and Pressure. However, we cannot control them perfectly and there is a chance that the output does not meet the minimum criteria even if we do our bests. In our production facility, the temperature follows a normal distribution with the mean of 110 F and the standard deviation of 20 F. The pressure also follows a normal distribution with the mean of 50 PSI and standard deviation of 25 PSI. Assume that temperature and pressure are independent. We will have an acceptable outcome if the temperature is between 130F to 140F and the pressure is higher than 90 PSI. What is the chance that we get an output that is acceptable?
4 – A group of students participated in a test. Almost 95% of them got a grade between 58 and 95. Assuming the grades are normally distributed, what are the mean and standard deviation of the grades?
5 – Students pass a test if they score 50% or more. The marks of a large number of students were sampled and the mean and standard deviation were calculated as 40% and 10% respectively.
Assuming this data is normally distributed, what percentage of students pass the test?
6 – Download and open the Excel file entitled “Data”. The file consists of 100 observations. If we assume that the data follows a normal distribution, could you find a range (i.e. a lower limit and an upper limit) that covers almost 68% of the observations?
7 – In a class consisting of 120 students, 65 students received “Certificate A”, 36 students received “Certificate B”. 24 students received both certificates (i.e. A and B). If you randomly select a student and you know that student has a certificate A, what is the probability that he/she also has a certificate B?
8 – The average grade in an exam in a class consisting of 62 students was 65 with the standard deviation of 12. The institution held a training workshop for the students and took another exam. This time the average grade is 72. With the significance level of 5%, is the increase in the average grade statistically significant?
To be consistent, let’s assume that the null hypothesis indicates that the average grade is still less or equal to 65.
9 -We conducted a multiple choice online survey about the reason that people went to a trip on two different websites: Amazon Mechanical Turk and Qualtrics. The table below shows the results. With a significance level of 5%, can we claim that the websites are independent from the responses? In other words, does it matter which website do we use to get feedback from people?
Response Number of responses on Amazon Turk Number of responses on Qualtrics
Business 76 61
Attend a conference 43 36
Vacation 257 221
Visit friends and families 272 214
Attend school 4 5
Others 36 19
10 – Assume that we took a test from students in two different classes: Class A and Class B. There are 56 students in Class A and 130 student in Class B.
After the exam, we conducted a survey and asked if the exam was fair. 32 students in Class A and 85 students in Class B responded “Yes! The exam was fair”. At a 5% significance level, is there any statistically significant difference between the opinions in Class A and Class B?
11 – Assume that we had conducted a regression analysis to explain variations of submitted bid prices in transportation projects against several explanatory variables such as duration of the project, number of bidders, quantity of the job, and price of fuel. Significance level is 5%.
A) What is the next step to complete the regression analysis process?
B) The coefficients of “number of bidders” and “quantity” are negative while coefficient of the “price of fuel” is positive. Can you interpret them? What do you think about the relation between those explanatory variables and the dependent variable (i.e. submitted bid prices).
12 – A real-estate agent in New Hampshire wants to use a regression model to explain variations in selling price for new homes using square footage as a predictor of price. The following data in the table is used to create the model. Use the OLS procedure to create the model. Estimate its coefficients and R-Square. Interpret the results. What would you estimate the average price to be for a house with 1750 square feet? Prices are in thousands of dollars.
NOTE: You can use Excel functions, but you should not use the Regression tool in Excel for this question.
Sq. Footage (X) Price (Y)
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