Six people of different ages are getting in line to buy coffees. Compute the number of ways they can arrange themselves in line such that no three consecutive people are in increasing order of age, from front to back

1.8. Problem. (Sections 2.2-2.4) Three fair, six-sided dice colored red, green and blue are rolled. Calculate each of the following probabilities:

(a) The probability all three dice show the same face (“triples”).

(b) The probability that the red die shows a larger number than the green die.

(c) The probability that the red die shows a larger number than the green die and the green die shows a larger number than the blue die.

(d) The probability that the sum of the pips on all three dice is exactly 10.

(e) The probability that the sum of the pips on all three dice is less than 10.

(f) The probability that the sum of the pips on all three dice is greater than 10.

Discuss the three properties (characteristics) of data and explain some of the descriptive measures associated with each property.

1. The length of industrial filters is a quality characteristic of interest. Thirty samples,
   each of size 5, are chosen from the process. The data yields an average length of
   110 mm, with the process standard deviation estimated to be 4 mm.
   (a) Find the warning limits for a control chart for the average length.
   (b) Find the 3sigma control limits. What is the probability of a type I error?
   (c) If the process mean shifts to 112 mm, what are the chances of detecting this shift
   by the third sample drawn after the shift?
   (d) What is the chance of detecting the shift for the first time on the second sample
   point drawn after the shift?
   (e) What is the ARL for a shift in the process mean to 112 mm? How many samples,
   on average, would it take to detect a change in the process mean to 116 mm?

The landing of military fighter jets on aircraft carrier requires great skill, so on occasions it requires more than one attempt to achieve the landing. TOP GUN is a pilot who is assigned to an aircraft carrier and has a record of achieving 95 % of landings on aircraft carriers in the first attempt. In a particular exercise TOP GUN is assigned to make four (4) takeoffs and landings on the aircraft carrier to which it is assigned. Under the assumption that the resulting events in each landing attempt are statistically independent of each other determine:

Most import: without using the binomial distribution. *NO BINOMIAL DISTRIBUTION*

a) The probability that TOP GUN achieve four (4) landings in the first (1) try.

b) The probability that TOP GUN achieve at least one (1) landing out of the four (4) on the first try.

This is an extension of the Birthday Problem. Suppose you have 500 Facebook friends. Make the same assumptions here as in the Birthday Problem.

a) Write a program in R to estimate the probability that, on at least 1 day during the year, Facebooks tells you three (or more) of your friends shat that birthday. Based on your answer, should you be surprised by this occurrence?

b) Write a program in R to estimate the probability that, on at least 1 day during the year, Facebook tells you five (or more) of your friends share that birthday. Based on your answer, should you be surprised by the occurrence? [Hint: Generate 500 birthdays with replacement, then determine whether any birthday occurs three or more times (five or more for part (b)). The table function in R may prove useful.]

The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 84.3 seconds. A manager devises a new drive-through system that he believes will decrease wait time. He initiates the new system at his restaurant and measures the wait time for ten randomly selected orders. The wait times are provided in the table below. Based on the given data, is the new system effective? Use the α = 0.10 level of significance.

On a separate sheet of paper, write down the hypotheses (H₀ and H_a) to be tested.

Conditions:
Use Minitab Express to perform a normality test on the given data.
The P-value for the Anderson-Darling test of normality is ______ (Report this value exactly as it appears in Minitab Express. Do not round.)
Based on both the normal probability plot and this P-value, the t-test for means  (is / is not) valid for the given data.

Rejection Region:
To test the given hypotheses, we will use a (left / right / two) -tailed test. The appropriate critical value(s) for this test is/are _________ .  (Report your answer exactly as it appears in Table VI. For two-tailed tests, report both critical values in the answer blank separated by only a single space.)

Hypothetical Human population matrix over a period of time of 20 year intervals.

Age 0-20 20-40 40-60 60-80   

0-20 [ .24 .98 0 0]

20-40 [ .77 0 .92 0]

40-60 [ .04 0 0 .57]

60-80 [ 0 0 0   0]

Complete the calculation to determine what the population distribution will be 200 years after the initial probability distribution shown in the example as P= [1000, 1000, 1000, 1000]. The formula is P*T^10 (there are 10 sets of 20 in 200)

After 200 years, # of people in the 0-20 range = _______________?

After 200 years, # of people in the 20-40 range = _______________?

After 200 years, # of people in the 40-60 range = _______________?

After 200 years, # of people in the 60-80 range = _______________?

Now, using the same population dynamics matrix, determine what the probability distribution will be after 320 yrars if the initial probability distribution is P= [1100, 1700, 1100, 1000] ? The formula is P*T^16 (there are 16 sets of 20 in 320)

After 320 years, # of people in the 0-20 range = _______________?

After 320 years, # of people in the 20-40 range = _______________?

After 320 years, # of people in the 40-60 range = _______________?

After 320 years, # of people in the 60-80 range = _______________?

In August 2003, 56% of employed adults in the United States reported that basic mathematical skills were critical or very important to their job. The supervisor of the job placement office at a 4-year college thinks this percentage has increased due to increased use of technology in the workplace. He takes a random sample of 530 employed adults and finds that 324 of them feel that basic mathematical skills are critical or very important to their job. Is there sufficient evidence to conclude that the proportion of employed adults who feel basic mathematical skills are critical or very important to their job has increased at the α = 0.01 level of significance?

The sample proportion is p^ =______- . (Round to 3 decimal places.)
The test statistic for this test is z₀=_______.  (Calculate this value in a single step in your calculator using the rounded sample proportion reported above, and report your answer rounded to 3 decimal places.)

We  (reject / fail to reject) H₀.
The given data  (does / does not) provide significant evidence that the proportion of employed adults who feel that basic mathematical skills are critical or very important to their job has increased since August 2003.

A supermarket chain analyzed data on sales of a particular brand of snack cracker

at 104 stores for a certain one week period. The analyst decided to build a regresion model to predict the sales of the snack cracker based on the total sales of all brands in the snack cracker category.

d. Make a prediction for sales in a week where sales in the entire snack

    cracker category is 1005.

Appraise what new statistical methods are used in the evaluation of conceptual theories outlining specific advantages these methods provide. Compare Structural Equation Modeling (SEM) techniques providing advantages of using SEM to other conventional methods outlining some of the various statistical techniques that SEM is able to perform. Evaluate sampling techniques used to conduct hypothetical studies and asses the benefits of each sampling method based on best fit to application. Critique validity and reliability methods for appropriate constructs and compare advantages and disadvantages of each method describing what methods to use with different operational techniques. Compare and evaluate factor analysis for confirmatory versus exploratory methods and assess when each is appropriate proving examples and application usages. Assess the differences of various regression analysis methods and demonstrate by examples what regression methods are most appropriate for different application. Finally discuss and recommend best statistical techniques and methods to operationally use for means comparisons, non parametric evaluation, bivariate correlation, ANOVAs, Chi Square, regression, and other techniques as appropriate. Assess the overall concept of statistical power, why it has import to statistical evaluations, and what SPSS contributes to statistical analysis in today’s research.

A supermarket chain analyzed data on sales of a particular brand of snack cracker

at 104 stores for a certain one week period. The analyst decided to build a regresion model to predict the sales of the snack cracker based on the total sales of all brands in the snack cracker category.

b. Is there sufficient evidence at 2.5% significance level to claim that linear

    relationship exists between category sales and cracker sales? Show the

   test, and make the conclusion.

Which probability rule would be used to determine the probability of getting into both your first choice graduate program AND getting an interview at your first choice post-graduation?

Solve for the probability of BOTH events occuring if the probability of getting into your first choice graduate program is estimated to be 25% and getting an interview at your first choice job post-graduation is estimated to be 50%.

If the robt = 0.20 and the df = 70 and the test was two-tailed, what is the rcv ?

Given the values provided in #17, should you reject or fail to reject the null hypothesis?

Significance level is 0.05

Choose the correct answer.

1. What is the percentile rank of 60 in the distribution of N(60, 100)?

a. 10

b. 50

c. 60

d. 100

1. The skewness value for a set of data is +2.75. This indicates that the distribution of scores is which one of the following?

   1. Highly negatively skewed

   2. Slightly negatively skewed

   3. Symmetrical

   4. Slightly positively skewed

   5. Highly negatively skewed

2. For a normal distribution, all percentiles above the 50th must yield positive z-scores. Is this true or false?

3. The distribution of variable X has a mean of 10 and is positively skewed. The distribution of variable Y has the same mean of 10 and is negatively skewed. Are the medians for the two variables the same or different?

A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, four guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.]