Reference no: EM132253438

Questions -

Q1. Respond to the following questions referring to normal distribution.

a. Which statistical measures define normal distribution completely?

b. Which values do these measures take in case of a standard normal distribution?

c. What percentage of observations in case of a normal distributed variable are approximately within z-score range of -1 and 2?

d. You observe a normal distributed variable with the mean (M) of 10 and standard deviation (s) of 1. The probability for a randomly chosen observation of that variable within z-score range -1 and 1 is approximately 68 percentage. What is the probability of a randomly chosen observation of that variable within the same z-score range if the standard deviation increases by factor 4 (s=4) while the distribution and mean do not change? Why?

Q2. You roll a die 1000 times and note the value that is obtained each time. The die can take the values 1, 2, 3, 4, 5, 6 whereat the probability of obtaining each of the values is the same 1/6.

a. What kind of a distribution do you expect for the 1000 values that you obtained?

b. Is the variable (values obtained by rolling the die) a continuous variable? Why?

c. You roll the die 10 times, note the values obtained, take the mean of those values and repeat the same procedure 50 times. Doing that you obtain 50 values each being the mean value calculated with the values obtained by 10 times rolling the die. What kind of a distribution do you expect for the mean values? Why?

d. Assume you have followed the procedure from b. and calculated the standard error. How would the standard error change if you would have followed the procedure from b. by throwing the dive 5 times each round instead of 10 times?

Q3. A company draws a random sample from the population of its customers to conduct a survey about the perception of the quality for its services. The customers provide their feedback by choosing a value on a Likert scale with a range from 0 to 10, being 0 not satisfied at all and 10 satisfied completely. Assume that the collected data is normal distributed and the population of the customers has the parameters μ = 6 and σ = 1.8. For each X value calculate the z-score: (provide the formula, set the values in the formula and round your results to 3 digits after coma if necessary)

a. X = 3.7

b. X = 5.2

c. X = 6

d. X = 8.5

Q4. Now calculate for the company from task 3 the margin of error (MoE) at the confidence level (C) of 95 for the following number of surveyed customers (population parameter remain the same) and provide a short explanation (1-2 sentences) of how and why MoE changes as the number of surveyed customers increase: (provide the formula, set the values in the formula and round your results to 3 digits after coma if necessary)

a. N = 16

b. N = 36

c. N = 49

d. N = 81

Q5. You draw a random sample of students attending the course intermediate quantitative research methods and observe their grades (in percentage) for their first Assignment. The grades are available in the table below. Be aware that you do not know σ (use the t-score from the lecture slides). (Provide the formula, set the values in the formula and round your results to 3 digits after coma if necessary).

a. Calculate the variance (V) and the standard deviation (s).

b. Calculate the confidence interval at the confidence level 95.

c. Provide 2 different interpretations of the confidence interval that you have calculated.

Q6. Provide a dofile and a logfile for the following tasks:

a. Execute the standard commands at the beginning of your dofile.

b. Create a working folder with the name "Ass2_QuantitativeMethods" and ensure that Stata uses this folder as working directory.

c. Start/Create a logfile with the name "Ass2_logfile_ Yourfamilyname".

d. Load the file "auto.dta" in to working storage (the file "auto.dta" is available in Stata as a system file).

e. Create a histogram for the variable "trunk" with 12 bins, showing percentage on the y axis. (save the histogram manually in png format and place it in your word document)

f. Create a dotplot for the variable "trunk" that distinguishes between foreign and domestic cars and also shows median as well as first and last quartiles. (0.5) (save the dotplot manually in png format and place it in your word document).

g. Figure out how to get the confidence interval information for the mean values of the variables price, mpg, and weight by using the help function of Stata "help ci" (opening the help function does not need to be in the dofile). Execute the command to show the confidence intervals for those variables.

h. Close the logfile and end the dofile.

Instructions: Please use short answers unless it is asked to do an explanation.