# Statistics questions

**Exercises for Section 4.1**

Use the hospital charge sheet in the file Chpt 4-1.xls

- Select the variable Age and do the following:

- Using =MIN ( ) , =MAX ( ) , and =FREQUENCY ( ) functions, replicate Figure 4.2.

- Using the results just obtained, generate the chart shown in Figure 4.8 and put in the relevant labels as shown in that chart. Show this chart on the spreadsheet.

- Modifying the data as shown in Figure 4.9, generate a line chart as shown in the figure and show this on the spreadsheet.

- Create a bar chart as shown in Figure 4.10 and show this on the spreadsheet.

- Create a pie chart as shown in Figure 4.11 and modify it to look as much like that figure as possible; show this on the spreadsheet.

- Use the SWC worksheet in the file Chpt 4-1.xls and do the following:

- Generate the appropriate frequency distribution for infant mortality (IMR) and with it replicate Figure 4.18
- Generate a frequency distribution of five Bin for under-five mortality (USMR) and produce a column graph for that variable. Is it normal, flat, or skewed, and if it is skewed, in which direction?

**Exercises for Section 4.2**

- Use the variable Sex on the Hospital Charges sheet in Chpt 4-1.xls and do the following
- Create a frequency distribution using the pivot table that replicates the one in Figure 4.26, using Count of Sex in the DATA field
- Create a frequency distribution using the pivot table that replicates the one in Figure 4.26, using Count of Age in the DATA field
- Is there any difference between the two tables you just created? Why or why not?

**Exercise for 4.3**

- Use the data on the MS-DRG worksheet in Chpt 4-2.xls and use the pivot table capability to replicate Figure 4.34

**Exercises for 5.1**

- Calculate the probability of the following

- The sequential roll of the die faces 2,4, and 3
- The sequence of coins flips HTHH
- Assuming a probability of any arrival at an emergency room being an emergency as 0.646, and assuming that arrivals are independent, the probability of the next four arrivals being all emergencies
- Assuming (c), the probability of the next five arrivals’ being all non emergencies
- Assuming (c), the probability of the next four arrivals’ bring two emergencies and two non emergencies, in that order
- Assuming a probability of 0.5 that any child born will be a boy, the probability of any family of five children having no girls

**Exercises for 5.2**

- Use the data in file Chpt 5-2.xls. This is the data file from which the discussion in Section 5.2 was developed. Do the following:

a. Generate a contingency table such as that shown in Figure 5.6, using the pivot table capability of Excel

- Calculate the marginal probabilities for both Shift and Emergency Status, as its shown in Figure 5.7

- Calculate the joint probabilities “and” for each of the cells in the table, as is shown in Figure 5.7. Confirm that the sum of cells is 1.

- Calculate the joint probabilities “or” for each of the cells in the table, as is shown in Figure 5.9. Confirm that the sum of the joint probabilities “or” is equal to rows + columns – 1.

- Calculate the conditional probabilities of reason for arrival, given that the patient arrives in the first, second, or third shift (replicate Figure 5.10) and confirm that reason for arrival and time of arrival are not independent.

**Exercises for 5.3**

- Use Equation 5.6 to determine the probability of any one outcome of the following:

*n =*5*, x =*2*, p =*0.646*n =*11,*x =*9,*p =*0.42

- Use Equation 5.7 to determine the number of separate outcomes for the following:

*n*= 5,*x*= 2*n*= 11,*x*= 9

3. Use Equation 5.8 to determine the binomial probability of the following:

*n =*5,*x =*2,*p =*0.646*n =*11,*x =*9,*p =*0.42

4. Use the =BINOMDIST ( ) function to determine the binomial probability of the following and determine if the are the same as what is given in Exercise 3.

*n =*5,*x =*2,*p =*0.646*n*= 11,*x*= 9,*p*= 0.42

- A dentist sees about fifteen new patients per month (the rest of her patients are repeats). She knows that on average, over the past year, about half of her patients have needed at least one filling on their first visit.

- What is the probability that she will see ten patients or more out of fifteen who need fillings?
- What is the probability that she will see five or fewer patients who need fillings?
- What is the probability that she will see between seven and ten new patients who need fillings?

**Exercises for 5.4**

2. Calculate the Poisson probabilities of finding unusable gloves in a box of one hundred if the average is two per box

- Using the =POISSON ( ) function
- Using the Poisson formula shown in Equation 5.9
- Replicate the chart in Figure 5.23.