Question

Please Answer ONLY F1, F2 and G .

Thanks

Problem: Daycare Management You've been hired as the Chief Statistician for the SummerlsFun Co. The corporation operates a variety of Summer Children Camp/Daycare chains: ParentsOasis SunAndPlay NoPlaceLikeHome As part of their ongoing marketing effort, SummerIsFun Co. collects a variety of statistics about their members. The database includes the following data (a) Child's age category: infant, toddlers, preschool, pre-K к} (b) Child's BMI category: underweight, normal weight overweight, obese (e) Number of diapers/week (if needed) used by the child (d) Child's year of birth. (e) Child's favored snack {fruits, cereals, crackers ( Child's household annual salary () Child's weight and height on the enrollment day, approximated to 1 decimal (b) Child's number of siblings enrolled in the same camp () Child's Preferred room temperature (in F) Does the child have allergies? {yes no IA (10 points) For cach of the questions, indicate with an "X" what scale the data is measured on. Question Nominal Ordinal Interval Ratio ka) b) kd) key kgx kh) ki B (10 points) For each of the questions, indicate with an "X" if the measurement is Qualitative, Quantitative Discrete or Quantitative Continuous. Question Qualitative Quantitative Discrete Quantitative Continuous. a) b) kd) el kh) C(11 points) The SummerlsFun Co. decided to use 20 different water balloon categories. Their prices (on 100 units) are listed below 27 25 10 7 20 27 15 25 10 13 22 16 11 9 12 20 17 17 23 20 a. Construct a grouped frequency distribution with 6 classes. Step 1. Find Range Step 2. Given the number of classes, the width of each class is Step 3. Create class boundaries Step 4. Find the numerical frequencies b. Use Excel to construct a Histogram. (Tools à Data Analysis à Histogram à for the input range, select the given values, for the bin range select the classes upper boundaries values à check Chart Output) Note: If you don't have the capability of using excel for the histogram, draw one by hand. D(14 points) Consider the following set of data containing the amount of paid tuition/week for part-timers: Amount 7-Score 70 80 55 75 55 75 80 85 60 85 a. For the set of data given above, calculate the following descriptive statistics (Briefly explain, especially the quartiles calculations. Use the rules given in the homework 2). For the rest you can use excel tools as long as you show your work. Mean Median Mode Who is in the lowest quartile? Explain Who is in the uppermost quartile? Interquartile Range Range Standard Deviation Variance b. Compute the z-scores and enter them in the first given table. Give the formula you used c. What type of skewness does this data set have? E (6 points) SummerlsFun Co will run a promotional raffle that offers a chance to win either a lifetime discount on merchandises (which results in a $1,000 savings) ora 5-year limited disccount on any party-goods (which results in a $100 savings) Winning a lifetime discount has a 1-in-500 chance Winning a 5-year limited discount has a 1-in-50 chance. Is this promotion worth it if the tickets cost $15? [F1 (13 points) Some additional collected data is presented in the table below Enrollment Infants ()Toddler (2-3Y) (T) Prek_K (K)| Camp/DayCare ParentsOasis (PO) SunAndFun (SF) NoPlaceLikeHome (NH) 10 10 50 0 20 32 20 40 Give the literal formula first (not with numbers) and then solve: "what is the probability of not being a Toddler?" Give the literal formula first (not with numbers) and then solve: What is the probability of being an infant or toddler given that you are attending the NoPlaceLikeHome camp?" Give the literal formula first (not with numbers) and then solve: "what is the probability of being a Pre-K_K child attending ParentsOasis camp?" Give the literal formula first (not with numbers) and then solve: What is the probability of being in the Toddler or PreK_K group and attending SunAndFun." Is there any relationship between being toddler and attending a specific Camp/Daycare? Explain based on "given" probabilities values. a F2. Partial Credit. Answer to it ONLY if you cannot answer F1 Another survey examines the parent's preference in having lunch provided by the SummerIsFun Co. or Iunch brought from home, based on their children's age. Some parents might not care, any possibility is OK. Camp/Daycare Food (D) Home Food (H) Parent (Infant/Toddler) IT Parent (pre-K,K) PK 50 100 85 65 a) Compute the Marginal Probabilities and the Joint Probabilities Joint probabilities: Marginal probabilities: b) Compute: P(IT H), P(IT or D) IG(28 points) Overall, the amount of days attended (per summer) is normally distributed around 35 days with a standard deviation of 4 days What's the probability that the number of attended days will be above 28? What percentile does an attendance of 35 days rank at? What is the probability of attending between 33 and 39 days? The parents with children at or below the 10 % ile of number of days attended need to bring an explanatory note. What will be the threshold of 10%? How likely (what is the probability) is it to have the number of days attended less than 30? Children that are in the top 15 % of attendance will receive a ticket to see the BubbleClown. What is the minimum number of days of attendance in order to receive such a ticket? If 49 children (49 size of the sample) selected randomly attend the summer cam likelihood that their mean number of attended days will be within 2 days of the population mean? what's the

Answer 1

F1)

Enrollment	Infants (I)	Toddler (T)	PreK_K (K)
Camp/Daycare				Total
ParentsOasis(PO)	0	10	50	60
SunAndFun(SF)	8	32	20	60
NoPlaceLikeHome(NH)	10	20	40	70
Total	18	62	110	190

Probability of not being a Toddler

Using the probability formula,

P(A)Number of favorable events Number of total events

62 Toddler) 1-P(Note being a Toddler) = 1- 100 P(Note being 0.38 a

Probability of being an infants or toddler given that you are attending the NoPlaceLikeHome

Using the law of conditional probability

P(A and Bl P(B) P(A|B)

and law of sum two independent events,

P(X or Y P(X)PY)

Now,

P((I or T) and NH) P((I or T)NH) P(NH)

P((I or T) and NH)-P(I and NH)+P(T and NH)-P(I and NH) and (T and NH))

20 10 20 P((I or T) and NH) 0.1524 + 190 190 X 190 190 _

70 0.3684 P(NH) 190

$\text{P((I or T)}|\text{NH)}= \frac{0.1524}{0.3684}=0.4135$

Probability of being a Pre-K_K child attending ParentsOasis camp

Using the probability formula,

P(A)Number of favorable events Number of total events

50 0.2632 190 P(PO and K)

Relationship between Toddler and attending specific DayCare

Camp/Daycare	Toddler (T)	Probability
ParentsOasis(PO)	10	0.1613
SunAndFun(SF)	32	0.5161
NoPlaceLikeHome(NH)	20	0.3226
Total	62

Most of the toddler attending SunAndFun DayCare.

F2)

a)

	Camp/Daycare Food (D)	Home Food (H)	Total
Parent (Infant/Toddler)IT	50	100	150
Parent (pre-K.K)PK	85	65	150
Total	135	165	300

The joint probabilities are,

joint probabilities
	Camp/Daycare Food (D)	Home Food (H)
Parent (Infant/Toddler)IT	0.1667	0.3333
Parent (pre-K.K)PK	0.2833	0.2167

And the marginal probabilities are,

	Camp/Daycare Food (D)	Home Food (H)	Total
Parent (Infant/Toddler)IT	0.1667	0.3333	0.5000
Parent (pre-K.K)PK	0.2833	0.2167	0.5000
Total	0.4500	0.5500	1.0000

Marginal probabilities
Parent (Infant/Toddler)IT	0.5000
Parent (pre-K.K)PK	0.5000
Camp/Daycare Food (D)	0.4500
Home Food (H)	0.5500

b)

100 0.3333 P(IT H)P(IT and H) 300

$\text{P(IT or D)}=\text{P(IT)}+\text{P(D)}-\text{P(IT and D)}$

135 150 50 P(IT or D) 0.7833 300 300 300