Question

1. For each of the following random variables, determine whether the variable is quantitative or qualitative. Further classify those variables as discrete/continuous or ordinal/nominal (a) Number of telephones per householod (b) Whether there is a fax machine in the household (c) Length (in minutes) of longest local call per month (d) Total time spent on online purchases in a month (e) Educational level of a person 2. It is believed that exercising can lower blood pressure. A medical researcher who impressed with this claim wanted to determine whether it is true. He randomly selected 1000 individuals, then divided them into two categories: individuals who are doing low level of exercise and individuals who are doing high level of exercise All the individuals are then interviewed about their exercise habits and measured their blood pressure (a) Is this an observational study or a designed experiment? Explain your reasoning (b) The medical researcher noticed that on average, the individuals who are doing low level of excrcise had considerably high blood pressure than the individuals who are doing high level of exercise. Therefore, he concluded that exercising can lower blood pressure. Do you think this is a good conclusion? Explairn your reasoning. Problems 3 and 4, you need to do by hand. Simplify the final answer and record to three decimal places. All summary measurements should include the notation and corresponding units. Clearly show your work 3. Following are the scores (out of 10) of a quiz for 10 randomly chosen students from a MATH 318 class 0, 5, 6.5,7,7.7.5. 8,8,9, 10 (a) Calculate the sample mean, sample variance, sample standard deviation, median, and the range for the quiz scores (b) Draw a dotplot (c) based on parts (a) and (b), would you believe this is a difficult quiz? Explain vour annswer.

Answer 1

1.a) Quantitative and discrete

b)Qualitative and ordinal( as order doesn't matter here)

c)Quantitative and continuous(as time can be 20.43 mins)

d) Quantitative and continuous

e) Qualitative and nominal (as order matters)

2.a)This is an observational study.In this type of study, the researcher relies more on data collected.
In observational study, the researcher just observes what has happened in the past and what is happening now and draws conclusions based on these data. But in experiments, the researcher observes things through various studies.

b) Conclusions based on observational study are not good especially due to the problem of lurking variables.For example: There might be some other reasons like Smoking,Being overweight or obese,Lack of physical activity,Too much salt in the diet,Too much alcohol consumption (more than 1 to 2 drinks per day),Stress,Older age,Genetics, Familyhistory of high blood pressure which or not included in the study and can effect the result greatly.

3. Sample mean= (0+5+6.5+7+7+7.5+8+8+9+10)/10 =6.8

Sample variance=((0-6.8)²+(5-6.8)²+(6.5-6.8)²+.....+(10-6.8)²/10 = 68.5716/10 = 6.85716

Sample standard deviation=√(6.86716) = 2.6186179

Median: Since we have even numbers of observations

So median is average of middle two numbers i.e.

(7+7.5)/2 = 7.25

Range :10-0 = 10.