Complete this vocabulary

1-p-hat

2-sample

3-chance model

4-Statistic ( not statistics )

5-Simulate

6-Strength of evidence

7-Observational units

8-Variable

9-Parameter

10- Plausible

The life time X of a component, costing $1000, is modelled using an exponential distribution with a mean of 5 years. If the component fails during the first year, the manufacturer agrees to give a full refund. If the component fails during the second year, the manufacturer agrees to give a 50% refund. If the component fails after the second year, but before the fifth year the manufacturer agrees to give a 10% refund.

(a) What is the probability that the component lasts more than 1 year?

(b) What is the probability that the component lasts between 2 years and 5 years?

(c) A particular component has already lasted 1 year. What is the probability that it will last at least 5 years, given it has already lasted 1 year?

(d) If the manufacturer sells one component, what should they expect to pay in refunds?

(e) If the manufacturer sells 1000 components, what should they expect to pay in refunds?

a. By hand, make an ordered stemplot of the distribution of the variable MothersAge for the female students. Show both your rough and final version of the stemplot. Use stems of five (See the Notes for an explanation of what stems of five are). There are 63 female students.

Mother's age 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,51

Female 1, 0, 2, 2, 3, 4, 7, 3, 2, 4, 7, 1, 6, 4, 5, 3, 1, 4, 0, 1, 1, 1, 0, 1, 0

Use the stem and leaf plots that you previously created to help you draw and label histograms on your scratch paper with bin width of 2 for mothers's age at birth of female students and for mother's age at birth of male students. Make the lower bound of your first bin 16.

Comment: Bin width of 2 is not a typo. Yes, your stem and leaf plot has bins of 5 so some thinking is required, but at least your stem and leaf plot has the values in order for you.

If nequals=100 and Xequals=35​, construct a 95​% confidence interval estimate of the population proportion.

A plastic bag manufacturer claims that the bags have a tear resistance (in Kg.) that is distributed N(10, 1):

a) We take 9 bags and get an average tear resistance of 9.5 Kg. ¿Should we believe the specifications provided by the manufacturer?

b) Find the probability that the bag will tear with 5 Kg. of oranges and 4 bottles of 1 liter of water whose containers weight 25 grs.

Develop a simulation model for a three-year financial analysis of total profit based on the following data and information. Sales volume in the first year is estimated to be 100,000 units and is projected to grow at a rate that is normally distributed with a mean of 7% per year and a standard deviation of 4%. The selling price is $10, and the price increase is normally distributed with a mean of $0.50 and standard deviation of $0.05 each year. Per-unit variable costs are $3, and annual fixed costs are $200,000. Per-unit costs are expected to increase by an amount normally distributed with a mean of 5% per year and standard deviation of 2%. Fixed costs are expected to increase following a normal distribution with a mean of 10% per year and standard deviation of 3%. Based on 500 simulation trials, compute summary statistics for the average three-year undiscounted cumulative profit. The question is from following book and from Chapter 12 question 22 Textbook: James Evans, Business Analytics, 3nd edition, 2019, Pearson Education, Pearson. ISBN: 13:978-0-13-523167-8

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

      Ho:μ1=μ2Ho:μ1=μ2
      Ha:μ1>μ2Ha:μ1>μ2

You obtain the following two samples of data.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.
• There is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.
• The sample data support the claim that the first population mean is greater than the second population mean.
• There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

3. A clinical trial examined the effectiveness of aspirin in the treatment of cerebral ischemia(stroke). Patients were randomized into treatment and control groups. The study wasdouble-blind. After six months of treatment, the attending physicians evaluated eachpatient’s progress as either favorable or unfavorable. Of the 78 patients in the aspiringroup, 63 had favorable outcomes; 43 of the 77 control patients had favorable outcomes.(A) The physicians conducting the study had concluded from previous research theaspirin was likely to increase the chance of a favorable outcome. Carry out a significancetest to confirm this conclusion. State the hypotheses, find aP-value, and write a summaryof your results.(B) Estimate the difference between the favorable proportions in the treatment andcontrol groups. Use 95% confidence.

A researcher interested in a relationship between self-esteem and depression conducted a study on undergraduate students and obtained a Person correlation of r = - 0.32, n = 25, p > .05 between these two variables. Based on this result the correct conclusion is _______.

• A. reject null hypothesis; there is a significant negative correlation between self-esteem and depression.

• B. reject null hypothesis; there is no significant correlation between self-esteem and depression.

• C. fail to reject null hypothesis; there is a significant negative correlation between self-esteem and depression.

• D. fail to reject null hypothesis; there is no significant correlation between self-esteem and depression.

1. Suppose we have the following annual sales data for an automobile dealership:

We want to forecast sales for 2019 and 2020 using either a simple trend model or a quadratic trend model. Use a within sample forecasting technique to determine the best model using the RMSE measure discussed in lecture. Once this model has been determined, provide actual forecasts for 2019 and 2020. Report the two RMSE values in your pdf or fax submission along with the actual forecasts. Submit your Excel file used to create these answers.

Customers at the local Subway store order an ice tea with their meal 75% of the time. Use the Binomial distribution to find the answer to the following. __________

Find the probability that among the next 8 customers, at least 3 will order ice tea with their meal: Of the next 8 customers, how many do you expect to order ice tea with their meal? __________

What is the standard deviation of the number of customers that order ice tea among the next 8 customers? (to two places after the decimal) _______

Customers using a self-service soda dispenser take an average of 12 ounces of soda with an SD of 4 ounces. Assume that the amount would be normally distributed.

What is the probability that a randomly selected customer takes over 8 ounces of soda?

0.25

0.84   

0.95

0.75

0.66

What is the probability that a randomly selected customer takes between 14 to 16 ounces of soda?

0.17

0.24   

0.14

0.15

0.85

How many of the next 100 customers will take an average of less than 12.48 ounces?

54

70

33

45

5

Suppose retailers would like to forecast the percentage of customers who plan to purchase gift cards during the upcoming holiday season. The following data show this percentage from 2002 to 2009. The data is as follows:

Perform the following:

1. Using a 3-period simple moving average, forecast the percentage of holiday shoppers who will purchase a gift card in 2010.

-

2. Calculate the MAD for the forecast in part a.

3. Using a 3-period weighted moving average with the weights 5, 3, and 1, forecast the percentage of holiday shoppers who will purchase a gift card in 2010.

4. Calculate the MAD for the forecast in part c.

5. In which forecast do you have the most confidence?