Use Excel and write formula of Chi square to Find the critical values check your answers with the tables of Chi square Critical Value:

   1- χ^2_(.05,25)
   2- χ^2_(.01,6)
   3- χ^2_(.05,10)

According to a report from Microsoft, 24% of PCs worldwide are not adequately protected by antivirus software.19 Suppose 200 PCs from around the world are selected at random.
a. Find the distribution of the sample proportion of PCs that
are not adequately protected.
b. Find the probability that the sample proportion is less
than 0.20.
c. Find the probability that the sample proportion is more
than 0.29.
d. Find a value v such that the probability the sample
proportion is less than v is 0.01.

Q1) construct a contingency table for the positive and non-positive returns of the two stocks

please construct on on excel.

In a baking competition between ten bakers, how many ways is it possible for the top three places, (1st -2nd - 3rd place) to be determined?

In a class of twenty students, how many ways are there to choose two students to participate in a debate?

A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below.

1. Find the correlation coefficient: r=r=   Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ? r ρ μ  == 0
   H1:H1: ? r ρ μ   ≠≠ 0
   The p-value is:    (Round to four decimal places)
   
3. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
   • There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful.
   • There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate.
   • There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days.
   • There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days .
4. r2r2 =  (Round to two decimal places)
5. Interpret r2r2 :
   • Given any group with a fixed number of vacation days taken, 71% of all of those employees will take the predicted number of sick days.
   • 71% of all employees will take the average number of sick days.
   • There is a large variation in the number of sick days employees take, but if you only look at employees who take a fixed number of vacation days, this variation on average is reduced by 71%.
   • There is a 71% chance that the regression line will be a good predictor for the number of sick days taken based on the number of vacation days taken.
6. The equation of the linear regression line is:   
   ˆyy^ =  + xx   (Please show your answers to two decimal places)
   
7. Use the model to predict the number of sick days taken for an employee who took 2 vacation days this year.
   Sick Days =  (Please round your answer to the nearest whole number.)
   
8. Interpret the slope of the regression line in the context of the question:
   • As x goes up, y goes down.
   • For every additional vacation day taken, employees tend to take on average 0.53 fewer sick days.
   • The slope has no practical meaning since a negative number cannot occur with vacation days and sick days.
9. Interpret the y-intercept in the context of the question:
   • If an employee takes no vacation days, then that employee will take 7 sick days.
   • The best prediction for an employee who doesn't take any vacation days is that the employee will take 7 sick days.
   • The y-intercept has no practical meaning for this study.
   • The average number of sick days is predicted to be 7.

Quick question, so say I have a mean of 511, a standard deviation of 124 and then I have less then 650. I do 650-511=139. I take the 139 and divide that by 124 and get 1.12. now with the z table that would become 0.8686, how do I do the z table because i am very confused on how to convert the answer to the z table.

Suppose we keep rolling a tetrahedral die (with faces marked as 1, 2, 3, 4) till an even number appears for the first time.

(a) Give a precise description of the sample space.

(b) Give the probability of each elementary outcome (each element of the sample space).

(c) Find the probability of an even number appearing for the first time at the nth roll.

(d) Find the probability of an even number appearing for the first time no later than the nth roll.

A dentist wants to find the average time taken by one of her hygienists to take X-ray and clean the tooth for her patients. She recorded the time to serve 24 randomly selected patients by the hygienist. The data of this experiment are save in the column “Time” of the SPSS file .

1. Compute the appropriate point estimate for population (true) mean time taken by this hygienist.

2. Construct a 98% confidence interval for the true average time taken by this hygienist.

3. The standard average for all the hygienists for this type of job is 34 minutes. Do the sample data provides evidence that the average time taken by the hygienist is longer than standard average for this job type? Use 1% significance level.                 

Please write how could I do it in SPSS

Consider the phrase "confidence interval" - what does the word "confidence" imply and what is the information provided by the word "interval"?

2. Three fair dice are rolled. Let X be the sum of the 3 dice.

(a) What is the range of values that X can have?

(b) Find the probabilities of the values occuring in part (a); that is, P(X = k) for each k in part (a). (Make a table.)

3. Let X denote the difference between the number of heads and the number of tails obtained when a coin is tossed n times.

(a) What are the possible values of X?

(b) Suppose that the coin is fair, and that n = 3. What are the probabilities associated with each of the values that X can take?

7. An urn holds 10 red and 6 green marbles. A fair coin is tossed. If we get heads, two marbles are selected from the urn. Otherwise three marbles are selected. If we have only reds, what is the probability that we selected exactly two marbles?

What are examples of:

1. Sampling Error.

2. Sampling Distribution of Sample Means

3. Central Limit Theorem.

4. Standard Error of the Mean. The standard error of the estimate of the mean is represented by the equation: σ√n Discuss what this equation means, using your own words and explain why we use it. Consider how it relates to the fact that we are making assumptions about the population and not just the sample.

Using MIL STD 105 E, probability of accepting a lot acceptance number when the lot size is 600,000 units, the inspection is normal general level I. Acceptance quality level is 0.025% and the proportion of defective product in the lots is 0.4%.

The correct answer is: 0.606.

Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.53 pounds and a standard deviation of 3.16 pounds.

a) What is the probability that the weight of a bag will be greater than the maximum allowable weight of 50 pounds? Give your answer to four decimal places.  

b) Let X represent the weight of a randomly selected bag. For what value of c is P(E(X) - c < X < E(X) + c)=0.96? Give your answer to four decimal places.  

c) Assume the weights of individual bags are independent. What is the expected number of bags out of a sample of 17 that weigh greater than 50 lbs? Give your answer to four decimal places.  

d) Assuming the weights of individual bags are independent, what is the probability that 8 or fewer bags weigh greater than 50 pounds in a sample of size 17? Give your answer to four decimal places.  

A random survey of enrollment at 35 community colleges across the United States yielded the following figures: 6,415; 1,549; 2,107; 9,348; 21,829; 4,300; 5,943; 5,724; 2,824; 2,043; 5,483; 5,199; 5,855; 2,749; 10,010; 6,359; 27,002; 9,416; 7,679; 3,201; 17,502; 9,202; 7,380; 18,313; 6,558; 13,714; 17,769; 7,491; 2,769; 2,862; 1,262; 7,283; 28,163; 5,082; 11,624. Assume the underlying population is normal.

• Part (a)

  Find the following. (Round your answers to the nearest whole number.)(i)    

  x =  

• s_x =  

• n = 35

• n − 1 = 34

• Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

• Part (d)

  Construct a 95% confidence interval for the population mean enrollment at community colleges in the United States.(i) State the confidence interval. (Round your answers to two decimal places.)

  ( , )

  
  
  (ii) Sketch the graph. (Round your answers to two decimal places. Enter your α/2 to three decimal places.)

  	CL = 0.95
  α 2 = 0.025		α 2 =0.025
  	0.05

  
  (iii) Calculate the error bound. (Round your answer to two decimal places.)