Start StatCrunch and make the following sequence selection: Applets -> Distribution demos. Next select "Binomial" and click "Compute!". In the resulting popup window experiment by using the sliders to assign approximately 0.5 to p and successively assign the values 20, 30 and 40 to n. Discuss what you see in the subsequently drawn Binomial Distribution defined by your specified values for n and p. What value on the x axis (horizontal axis) does the top of the hump of the curve correspond to. Next set p and n to their extreme values? Discuss what you observed using the fact that the x-axis represents the number of successes and the height of the vertical lines represent the probability of getting x number of successes.

Problem 16-13 (Algorithmic)

The wedding date for a couple is quickly approaching, and the wedding planner must provide the caterer an estimate of how many people will attend the reception so that the appropriate quantity of food is prepared for the buffet. The following table contains information on the number of RSVP guests for the 145 invitations. Unfortunately, the number of guests does not always correspond to the number of RSVPed guests.

Based on her experience, the wedding planner knows it is extremely rare for guests to attend a wedding if they notified that they will not be attending. Therefore, the wedding planner will assume that no one from these 50 invitations will attend. The wedding planner estimates that the each of the 25 guests planning to come solo has a 75% chance of attending alone, a 20% chance of not attending, and a 5% chance of bringing a companion. For each of the 60 RSVPs who plan to bring a companion, there is a 90% chance that she or he will attend with a companion, a 5% chance of attending solo, and a 5% chance of not attending at all. For the 10 people who have not responded, the wedding planner assumes that there is an 80% chance that each will not attend, a 15% chance each will attend alone, and a 5% chance each will attend with a companion.

1. Assist the wedding planner by constructing a spreadsheet simulation model to determine the expected number of guests who will attend the reception. Round your answer to 2 decimal places.
   
   guests
   
2. To be accommodating hosts, the couple has instructed the wedding planner to use the Monte Carlo simulation model to determine X, the minimum number of guests for which the caterer should prepare the meal, so that there is at least a 90% chance that the actual attendance is less than or equal to X. What is the best estimate for the value of X? Round your answer to the neares whole number.
   
   guests

1. Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

   1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.
      
      
      
   2. What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.
      
      
      
   3. What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00? If required, round your answer to the hundreds place.
      
      miles

1. Use the XLMiner Analysis ToolPak to find descriptive statistics for Sample 1 and Sample 2. Select "Descriptive Statistics" in the ToolPak, place your cursor in the "Input Range" box, and then select the cell range A1 to B16 in the sheet. Next, place your cursor in the Output Range box and then click cell D1 (or just type D1). Finally make sure "Grouped By Columns" is selected and all other check-boxes are selected. Click OK. Your descriptive statistics should now fill the shaded region of D1:G18. Use your output to fill in the blanks below.

   Sample 1 Mean:  (2 decimals)

   Sample 1 Standard Deviation:  (2 decimals)

   Sample 2 Mean:  (2 decimals)

   Sample 2 Standard Deviation:  (2 decimals)

2. Use a combination of native Excel functions, constructed formulas, and the XLMiner ToolPak to find covariance and correlation.

   In cell J3, find the covariance between Sample 1 and Sample 2 using the COVARIANCE.S function.

   (2 decimals)

   In cell J5, find the correlation between Sample 1 and Sample 2 using the CORREL function.
   (2 decimals)

   In cell J7, find the correlation between Sample 1 and Sample 2 algebraically, cov/(sx*sy), by constructing a formula using other cells that are necessary for the calculation.

   (2 decimals)

   Use the XLMiner Analysis ToolPak to find the correlation between Sample 1 and Sample 2. Place your output in cell I10.

   (2 decimals)

3. Calculate z-scores using a mix of relative and absolute cell references. In cell A22, insert the formula =ROUND((A2-$E$3)/$E$7,2). Next grab the lower-right corner of A22 and drag down to fill in the remaining green cells of A23 to A36. Note how the formula changes by looking in Column D. Changing a cell from a relative reference such as E3 to an absolute reference such as $E$3 means that cell remains "fixed" as you drag. Therefore the formula you entered into A22 takes each data observation such as A2, A3, A4..., subtracts $E$3 and then divides by $E$7. Since the last two cells have absolute references they will not change as you drag. The ROUND function simply rounds the z-score to two digits.

   Now find the z-scores for Sample 2 using the same method you learned above by editing the formula to refer to the correct cells for Sample 2. Make sure each z-score is rounded to 2 places.

   Sample 2 z-scores

Decisions about alpha level may be different, especially as it relates from hard sciences to social sciences. For example, medical trials for cancer treatments are conducted at an alpha of 0.0001. For "hard" and social sciences, alpha of 0.05 is used. Do you agree with these alpha levels? Why or why not? Provide a specific example and interpretation of "significance" in your answer.

Tommy has recently graduated from SUSS and has joined a well-known retailer that operates 3 department stores in Singapore. His job function is that of a business analyst. It has been well-reported that retail business in Singapore is on the decline and his employer would like to determine if the forecast for the next few years will be equally bad. Tommy has been tasked to perform the analysis and his output will provide insights in the company's hiring and expansion plan in Singapore.

The first thing Tommy did was to download the Retail Sales Index data from the Department of Statistics Singapore website. He specifically extracted the data for "Department Stores" from Q1 2008 to Q4 2018. (2017 is set as the base year with Index = 100). Refer to data below:

Year/Quarter Retail Sales Index (Department Stores)

2008 1Q 92.4

2008 2Q 93

2008 3Q 84.9

2008 4Q 105.3

2009 1Q 87.1

2009 2Q 88.6

2009 3Q 83.2

2009 4Q 103.6

2010 1Q 94.3

2010 2Q 93.9

2010 3Q 90.7

2010 4Q 109.3

2011 1Q 99.6

2011 2Q 99

2011 3Q 95.8

2011 4Q 119.3

2012 1Q 104.9

2012 2Q 99.9

2012 3Q 95

2012 4Q 117

2013 1Q 106.1

2013 2Q 100.9

2013 3Q 97.5

2013 4Q 118.6

2014 1Q 107.1

2014 2Q 98.7

2014 3Q 95.7

2014 4Q 117.6

2015 1Q 108.2

2015 2Q 101.1

2015 3Q 98.8

2015 4Q 114.4

2016 1Q 103.8

2016 2Q 93.9

2016 3Q 93.2

2016 4Q 112.9

2017 1Q 100.3

2017 2Q 93

2017 3Q 94.6

2017 4Q 112.1

2018 1Q 102.7

2018 2Q 92.3

2018 3Q 93.6

2018 4Q 112.8

(a) Use the techniques of time series modelling and with justifications, discuss the considerations on how Tommy would forecast the quarterly Retail Sales Index in 2019 and 2020.

(b) Upon confirmation of the forecast technique to undertake in Part 3(a), determine the quarterly RSI forecast in 2019 and 2020. You are required to show the essential steps in deriving the forecast and comment on any limitations of your technique.

• Explain the difference between two independent samples and two dependent samples.
• Provide examples of each type of pairs of samples.
• Compare and contrast the hypothesis testing process of two independent and two dependent samples. (Do not conduct the hypothesis testing.)

Known: Traffic averages 1825VPH

Standard deviation pf 375VPH

Sample of 20 days

A) Use a t distribution to determine the probability of traffic exceeding 2200 VPH and

B) Use a t distribution to determine the t value for where t <0.02 (2%).

A diet doctor claims Australians are, on average, overweight by more than 10kg. To test this claim, a random sample of 100 Australians were weighed, and the difference between their actual weight and their ideal weight was calculated and recorded.

The data are contained in the Excel file Weights.xlsx.

Use these data to test the doctor's claim at the 5% level of significance.

Question 10

(Part B)

In this question, we let μ represent

Question 11

(Part B)

The null hypothesis is

Question 12

(Part B)

The alternative hypothesis is

Question 13

(Part B)

The value of the t-statistic is

Question 14

(Part B)

The decision rule is

Question 15

(Part B)

The p-value is

Let U and V be independent continuous random variables uniformly distributed from 0 to 1. Let X = max(U, V). What is Cov(X, U)?

Question is based on the information given below: Annual Cancer Death in White Male Workers in Two Industries Industry A Industry B No. of Deaths % of All Cancer Deaths No. of Deaths % of All Cancer Deaths Respiratory system 180 33 248 45 Digestive system 160 29 160 29 Genitourinary 80 15 82 15 All other sites 130 23 60 11 Total 550 100 550 100 Based on the preceding information, it was concluded that workers in industry B are at higher risk of death from respiratory system cancer than workers in industry A. (Assume that the age distributions of the workers in the two industries are nearly identical.) 1. Which of the following statements is true? The conclusion reached in correct The conclusion reached may be incorrect because proportionate mortality rates were used when age-specific mortality rates were needed The conclusion reached may be incorrect because there was no comparison group The conclusion reach may be incorrect because proportionate mortality was used when cause-specific mortality rates were needed. None of the above

The mortality rate from disease X in city A is 75/100,000 in persons 65 to 69 years old. The mortality rate from the same disease in city B is 150/100,000in persons 65-69 years old. The inference that disease X is two times more prevalent in persons 65 to 69 years old in city B than it is in persons 65-69 years old in city A is: Correct Incorrect, because of failure to distinguish between prevalence and mortality Incorrect, because of failure to adjust for differences in age distributions Incorrect, because of failure to distinguish between period and point prevalence Incorrect, because a proportion is used when a rate is required to support the inference

Height Requirement Assignment

Use the given parameters to complete the assignment:

• Men's heights are normally distributed with mean 69.5 in. and standard deviation 2.4 inches.
• Women's heights are normally distributed with mean 63.8 in. and standard deviation 2.6 inches.

The U.S. Air Force requires pilots to have heights between 64 in. and 77 in.

Answer the following questions for the height requirement for U.S. Air Force pilots.

a) What percent of women meet the height requirements?
b) What percent of men meet the height requirements?
c) If the Air Force height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women, what are the new height requirements?

1. A study was conducted of recent high school graduates who began full-time jobs rather than going to college. We wish to find the average starting income µ of such workers. A random sample of size 60 gave a sample mean of $24,500 with a population standard deviation of $2350.Round answers to 2 decimal places.

1. Find the standard error.

2. Identify the upper and lower z score for a 95% confidence interval for µ.

3. Calculate the upper and lower bounds of the confidence interval.