For a 3 digit code with distinct numbers. (0-9)

How many combinations to get the code (max)?

How many combinations if you remember the middle number is 1?

Test whether profit for Massive Dynamic increased across the two time periods. You are not told anything about the population variances. Highlight the numbers that help you test the null hypothesis. In the text box below, explain whether once company has outperformed the other based on the evidence you provided in the last four spreadsheets. You need to reference the numbers you highlighted in your analysis. If you are concise, this should only take a few sentences. Note that I have not provided an α, so your analaysis should include a discussion about significance levels.

Please show how to do in Excel, thank you!

Discuss the reasons and situations in which researchers would want to use linear regression. How would a researcher know whether linear regression would be the appropriate statistical technique to use? What are some of the benefits of fitting the relationship between two variables to an equation for a straight line? Describe the error in the conclusion. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. As the number of cigarettes increases the pulse rate increases. Conclusion: Cigarettes cause the pulse rate to increase. Discuss causation vs. relationships.

The Culminating Project

Offering career academies in high schools has become more popular during the past 30 years because they help students prepare for work and postsecondary education. A principal at a large high school with a Science, Technology, Engineering, and Mathematics (STEM) Academy is interested in determining whether the status of a student is associated with level of participation in advanced placement (AP) courses. Student status is categorized as (1) STEM for students in the STEM program or (2) regular. A simple random sample of 200 students in the high school was taken and each student was asked two questions:

1. Are you in the STEM Academy?

2. In how many AP courses are you currently enrolled?

The responses of the 200 students are summarized in the table.

Part A: Calculate the proportion of STEM students who participate in at least one AP course and the proportion of regular students in the sample who participate in at least one AP course.

Part B: Is participating in two or more AP courses independent of student status?

Part C: Describe a method that could have been used to select a simple random sample of 200 students from the high school.

Part D: Is there any reason to believe there is bias in the method that you selected? Why or why not?

Part E: The responses of the 200 students are summarized in the segment bar graph shown.

Compare the distributions and what the graphs reveal about the association between level of participation in AP courses and student status among the 200 students in the sample. (5 points)

Part F: Do these data support the conjecture that student status is related to level of participation in AP courses? Give appropriate statistical evidence to support your conclusion. (10 points)

1. Assume that every time Jordan plays golf her score is normally distributed with mean 100 and standard deviation 6.
   1. Jordan is playing golf with her friend Joey who gets a score of 112. What is the probability that Jordan gets a score less than or equal to Joey's?
   2. Jordan is playing golf with another friend, Lillian, who gets a score of 106. What is the probability that Jordan gets a score greater than or equal to Lillian's?
   3. For what number is there an 84% probability that Jordan will get a score less than or equal to it? HINT: For instance, 100 is the number that Jordan has a 50% probability of scoring less than or equal to.
   4. These three friends decide to play four games of golf and record their average (mean) scores. Joey's average score is 94 and Lillian’s average score is 103. What is the probability that Jordan’s average score after playing four games of golf is between her two friends’ average scores (greater than or equal to Joey’s and less than or equal to Lillian’s)?

Use for Questions 1-7:

Hector will roll two fair, six-sided dice at the same time. Let A = the event that at least one die lands with the number 3 facing up. Let B = the event that the sum of the two dice is less than 5.

1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”?

2. Calculate the probability that at least one die lands with 3 facing up and the sum of the two dice is less than 5.

3. What is the correct set notation for the event that “at least one die lands with 3 facing up if the sum of the two dice is less than 5”?

4. Calculate the probability that at least one die lands with 3 facing up if the sum of the two dice is less than 5.

5. What is the correct set notation for the event that “the sum of the two dice is not less than 5 if at least one die lands with 3 facing up”?

6. Calculate the probability that the sum of the two dice is not less than 5 if at least one die lands with 3 facing up. 7. Are A and B independent? Explain your reasoning.

Use for question 10: A particular type of scan is used to try to determine whether brain tumors are cancerous or not. Each time a tumor is scanned, the result is reported as either “positive”, “negative” or “inconclusive”. Among tumors that are cancerous, 68% of scans are “positive”, 28% of scans are “inconclusive”, and 4% of scans are “negative”. Among tumors that are NOT cancerous, 60% of scans are “negative”, 37% of scans are “inconclusive” and 3% of scans are “positive”. Historically, among all brain tumors, 67% are not cancerous.

10. If a tumor is scanned and the result is labeled as “inconclusive” what is the probability that the tumor is not cancerous?

Find an example of use of a) cluster analysis and b) classification in research or business literature. Preferably, those example should be taken from the same domain. Analyze the problems that were solved with those two methods and the conclusions that were made.

In your initial post summarize both of the cases and highlight why each those methods were selected for each of the examples. Discuss the particular algorithms selection if it is provided. Draw a more general conclusion how to decide which method to use in the similar cases.

In what follows use any of the following tests/procedures: Regression, confidence intervals, one-sided t-test, or two-sided t-test. All the procedures should be done with 5% P-value or 95% confidence interval.

Use the Brains data. SETUP: Is it reasonable to claim that the average head circumference is less than 56?

5. What test/procedure did you perform?

• a. One-sided t-test
• b. Two-sided t-test
• c. Regression
• d. ​​Confidence interval

6. What is the P-value/margin of error?

• a. 2.30791
• b. 0.00166
• c. 4.72877
• d. 5.21228
• e. ​​None of these

7. Statistical interpretation

• a. We are 95% certain that the 56 is not within the confidence interval.
• b. Since P-value is small enough the above claim is reasonable.
• c. Since P-value is too large the above claim is not reasonable.
• d. ​​None of these.

8. Conclusion

• a. Yes, I am confident that the above claim is correct.
• b. No, we cannot claim that the above claim is correct.

DATA : https://www.limes.one/Content/DataFiles/Brains.txt

CCMIDSA: Corpus Collasum Surface Area (cm2)     FIQ: Full-Scale IQ      HC: Head Circumference (cm)     ORDER: Birth Order      PAIR: Pair ID (Genotype)        SEX: Sex (1=Male 2=Female)      TOTSA: Total Surface Area (cm2) TOTVOL: Total Brain Volume (cm3)        WEIGHT: Body Weight (kg)
8.42    96      57.2    1       6       1       1806.31 1079    61.236
7.44    88      57.2    1       7       1       2018.92 1104    79.38
6.84    85      57.2    1       8       1       2154.67 1439    99.792
6.48    97      57.2    1       9       1       1767.56 1029    81.648
6.43    124     58.5    1       10      1       1971.63 1160    72.576
7.62    101     57.2    2       6       1       1689.6  1173    61.236
6.03    93      57.2    2       7       1       2136.37 1067    83.916
6.59    94      55.8    2       8       1       1966.81 1347    97.524
7.52    114     56.5    2       9       1       1827.92 1100    88.452
7.67    113     59.2    2       10      1       1773.83 1204    79.38
6.08    96      54.7    1       1       2       1913.88 1005    57.607
5.73    87      53      1       2       2       1902.36 1035    64.184
6.22    101     57.8    1       3       2       2264.25 1281    63.958
5.8     103     56.6    1       4       2       1866.99 1051    133.358
7.99    127     53.1    1       5       2       1743.04 1034    62.143
7.99    89      54.2    2       1       2       1684.89 963     58.968
8.76    87      52.9    2       2       2       1860.24 1027    58.514
6.32    103     56.9    2       3       2       2216.4  1272    61.69
6.32    96      55.3    2       4       2       1850.64 1079    107.503
7.6     126     54.8    2       5       2       1709.3  1070    83.009

1. A recent report in Woman’s World magazine suggested that the typical family of four with an intermediate budget spends about $106 per week on food. The following frequency distribution was included in the report. Compute the mean, median, and standard deviation. How do your results compare with those of the report?

The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.30 A, with a sample standard deviation of s = 0.45 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

A. What are we testing in this problem?

single mean or single proportion  

B. What is the level of significance?

C. State the null and alternate hypotheses. (Out of the following): H₀: μ = 0.8; H₁: μ ≠ 0.8 ------ H₀: p = 0.8; H₁: p ≠ 0.8 ------ H₀: μ = 0.8; H₁: μ > 0.8 ----- H₀: p = 0.8; H₁: p > 0.8 ----- H₀: p ≠ 0.8; H₁: p = 0.8 ----- H₀: μ ≠ 0.8; H₁: μ = 0.8

D. What sampling distribution will you use? What assumptions are you making? (out of the following): The standard normal, since we assume that x has a normal distribution with unknown σ. ----- The standard normal, since we assume that x has a normal distribution with known σ. ----- The Student's t, since we assume that x has a normal distribution with known σ. ----- The Student's t, since we assume that x has a normal distribution with unknown σ.

E. What is the value of the sample test statistic? (Round your answer to three decimal places.)

F: Find (or estimate) the P-value. (Out of the following): P-value > 0.250 ----- 0.125 < P-value < 0.250 ----- 0.050 < P-value < 0.125 ----- 0.025 < P-value < 0.050 ----- 0.005 < P-value < 0.025 ----- P-value < 0.005

Provide an example of

What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula. .

A study determined 35% of Millennials in America have no credit card debt. By assuming p = .35 is a success (no debt), if a random sample of 50 millennials was selected, find the probability that 20 of them have no debt. Use the normal distribution as an approximation to solve this binomial problem.

Compute the approximate probability using the normal distribution. (Round to 2 places).