1) We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 16.
ii) One of 5 different suits.

Hence, there are 80 cards in the deck with 16 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get. a) How many different ways are there to get any 5 card hand?
The number of ways of getting any 5 card hand is
DO NOT USE ANY COMMAS

b)How many different ways are there to get exactly 1 pair (i.e. 2 cards with the same rank)?
The number of ways of getting exactly 1 pair is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 1 pair?
Round your answer to 7 decimal places.


c) How many different ways are there to get exactly 2 pair (i.e. 2 different sets of 2 cards with the same rank)?
The number of ways of getting exactly 2 pair is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 2 pair?
Round your answer to 7 decimal places.


d) How many different ways are there to get exactly 3 of a kind (i.e. 3 cards with the same rank)?
The number of ways of getting exactly 3 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 3 of a kind?
Round your answer to 7 decimal places.


e) How many different ways are there to get exactly 4 of a kind (i.e. 4 cards with the same rank)?
The number of ways of getting exactly 4 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 4 of a kind?
Round your answer to 7 decimal places.


f) How many different ways are there to get exactly 5 of a kind (i.e. 5 cards with the same rank)?
The number of ways of getting exactly 5 of a kind is
DO NOT USE ANY COMMAS

A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean μ = 38 minutes and standard deviation σ = 5 minutes. (a) The drug is administered to one patient selected at random. What is the probability that the time it takes to go into effect is 35 minutes or less? (Round your answer to four decimal places.) (b) The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less? (Round your answer to four decimal places.) (c) Comment on the differences of the results in parts (a) and (b). The probability in part (b) is part (a) because the is for the x distribution.

A consulting company is hired to investigate the relationship between average physician annual income and number of beds present at a local hospital. Assume the following table represents a SRS of hospitals.

1. Calculate basic descriptive statistics for your X and Y variables.

2. Calculate a correlation coefficient, and interpret your result with respect to strength and direction.

3. Calculate and correctly interpret your r² for the data.

4. Can we consider the relationship causal? For instance, can we claim that the higher the physician average income at a hospital, the more beds the hospital has?

An experimental drug is being tested to see if it reduces blood sugar in patients suffering from diabetes. Each of seven patients will receive both the placebo and the experimental drugs (treatments given a month apart) for a two week period. The maximum blood sugar (measured every day) on the second week of treatment is recorded. The data obtained from such a study is shown below:

Conduct a hypothesis test to determine whether the new experimental treatment is beneficial for treating diabetes.  

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. Find (or estimate) the P-value.

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 15.8 inches, and standard deviation of 4.7 inches.

If 35 items are chosen at random, what is the probability that their mean length is greater than 13.9 inches?

The data set is a study of student persistent enrolling in the next semester based on Gender, Age, GPA, a 22 questionnaire on self-efficacy, and student enrollment status.The educational researcher wants to study the relationship between student enrollment status as it relates to gender, age, GPA, and the total response to a 22 questionnaire survey.

2. The estimated multiple regression analysis equation.

3. Does the model work?

4. How well does the model work?

5. Which variables contribute to the model?

6. General interpretation of the data and the data analysis

After years of meteorological investigation, daily rainfall over a region in the North of India is supposed to be distributed as a Normal distribution with mean 22.6mm and variance 41.7mm2.

2. A day is classified as abnormally wet if rainfall levels are greater than or equal to 35mm. What is the probability of having an abnormally wet day?

3. A period of 14 days is considered. What is the probability that one abnormally wet day will be observed during this period?

Sixty students were asked during finals week to choose their favorite treat to eat while studying. They were given four choices (cake, cookies, ice cream, donuts) and asked to choose one. Their data were as follows:

Cake 10

Cookies 12

Ice Cream 20

Donuts 18

Using an alpha of .05, conduct a hypothesis test by hand using all steps of hypothesis testing to examine the following research question: Is there a difference in students’ preferred choice of treat? Go through all of the steps in hypothesis testing including:

a) State your hypotheses.

b) Find the df and critical value(s)

c) Compute the test statistic by hand

d) Make a decision

e) Calculate effect size, if needed

f) Write your results sentence(s). Include your test statistic in journal form

1. A polling organization talks to several people concerning what is their preferred method of obtaining political news.

The table breaks the information by age.

a. [3] What proportion of respondents

preferred where age 31 to 55 or preferred to get political news via internet sources?

b. [3] Of the respondents that preferred to get political news via printed publication what percentage where 56 and over?

c. [3] Show that the events a person is 18 to 30, a person prefers to get political news via television are not independent events.

My question is that should I accept or reject the null hypothesis?

Variable 1: General Health / Ordinal

Variable 2: Body Mass Index / Continuous

Null hypothesis: There is no statistically significant relationship between general health and body mass index. (In other words, correlation coefficient is equal or close to zero.)

Research/Alternative hypothesis: There is a statistically significant relationship between general health and body mass index. (In other words, correlation coefficient is different/far from zero.)

Statistical analysis used: Spearman’s (rank-order) correlation analysis

Key statistics:

Correlation coefficient: r = 0.248 (weak positive)

Statistical significance: p = 0.000 (statistically significant at level 0.01)

Coefficient of determination/Shared variance/Effect size/Practical significance (r2) = 0.248  * 0.248  = 0.062 (small)

0.062 *100= 6.2%. This means that 6.2% of the change/variance/variability in variable #1 (General Health)explains change/variance/variability in variable #2 (Body Mass Index). In other words, these two variables share 6.2% variance. This also means that 93.8% of variance in each of these variables remain unexplained/unaccounted for.

Assumptions:

1.Outliers: Scatterplot and boxplot show some significant outliers in the data.

2.Normality: Normality was assessed using Shapiro-Wilk’s test, and the distribution of the two variables are statistically significantly different from normal distribution (p = 0.000, p < .05).

3.Linearity: Scatterplot doesn’t demonstrate any linear relationship between these two variables (General Health and Body Mass Index). The scatterplot shows vertical lines with each category.

Accept or reject the null: Accept the null hypothesis and reject the research hypothesis. Although the p value show that data is statistically significant, the correlation coefficient is weak and effect size is small. Moreover, the data didn’t meet any of the assumptions.

My question is that should I accept or reject the null hypothesis?

. Four hundred melanoma patients were diagnosed according to the type of skin cancer and the location of the skin cancer. This data is presented below. What proportion of patients had superficial spreading melanoma? Of patients with a skin cancer on the trunk, what proportion had a nodular skin cancer? What proportion of patients had a Hutchinson’s melanomic freckle on the extremities? Is type of skin cancer independent of location? Justify your answer. Location Type Head and Neck Trunk Extremities Total Hutchinson’s melanomic freckle 22 2 10 34 Indeterminate 11 17 28 56 Nodular 19 33 73 125 Superficial spreading melanoma 16 54 115 185 Total 68 106 226 400

USE EXCEL TO SOLVE

Joan’s Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the planting of a medium sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours):

1.7 1.5 2.4 2.2 1.9 2.3 2.1 1.6 1.4 2.3

At the 10% significance level test using p-value method to see whether the mean tree-planting time is less than two hours?

List different properties one can use when describing the shape of the distribution.