A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows:

(a) Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary

X.

(Enter your answers for p(x) as fractions.)

(b) Suppose one of the three offices is randomly selected. Let X₁ and X₂ denote the salaries of the two employees. Determine the sampling distribution of

X.

(Enter your answers as fractions.)

(c) How does

E(X)

from parts (a) and (b) compare to the population mean salary μ?

E(X)

from part (a) is  ---Select--- greater than less than equal to μ, and

E(X)

from part (b) is  ---Select--- greater than less than equal to μ.

A sample of 43 observations is selected from a normal population. The sample mean is 60, and the population standard deviation is 8. Conduct the following test of hypothesis using the 0.02 significance level. H0: μ = 63 H1: μ ≠ 63

3. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
4. What is the p-value? (Round your z value to 2 decimal places and final answer to 4 decimal places.)
5. e-2. Interpret the p-value? (Round your z value to 2 decimal places and final answer to 2 decimal places

Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows.

(a)

Consider a random sample of size n = 2 (two customers), and let

X

be the sample mean number of packages shipped. Obtain the probability distribution of

X.

(b)

Refer to part (a) and calculate

P(X ≤ 2.5).

(c)

Again consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]

(d)

If a random sample of size n = 4 is selected, what is

P(X ≤ 1.5)?

[Hint: You should not have to list all possible outcomes, only those for which

x ≤ 1.5.]

There are two traffic lights on a commuter's route to and from work. Let X₁ be the number of lights at which the commuter must stop on his way to work, and X₂ be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X₁, X₂ is a random sample of size n = 2).

(a) Determine the pmf of T_o = X₁ + X₂.

(b) Calculate μ_To.
μ_To =

How does it relate to μ, the population mean?
μ_To =  · μ

(c) Calculate σ_To².

How does it relate to σ², the population variance?
σ_To² =  · σ²

(d) Let X₃ and X₄ be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T_o = the sum of all four X_i's, what now are the values of E(T_o) and V(T_o)?

(e) Referring back to (d), what are the values of

P(T_o = 8) and P(T_o ≥ 7)

[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)

An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.

(a) Compute the covariance for X and Y. (Round your answer to two decimal places.)
Cov(X, Y) =

(b) Compute ρ for X and Y. (Round your answer to two decimal places.)
ρ =

A scientist wants to determine whether or not the height of cacti, in feet, in Africa is significantly higher than the height of Mexican cacti. He selects random samples from both regions and obtains the following data.

Africa:
Mean = 12.1
Sample size = 201

Mexico:
Mean = 11.2
Sample size = 238

(a) Which of the following would be the correct hypothesis test procedure to determine if the height of cacti, in feet, in Africa is significantly higher than the height of Mexican cacti?

Paired t-testTwo-sample test for proportions    Two-sample t-test

(b) What is the value of the sample statistic to test those hypotheses?  (2 decimal places)

(c) If the T test statistic is 2.169, and df = 202, find the p-value.  (3 decimal places)


(d) Select the correct conclusion at alpha = 0.05.

The null hypothesis is rejected. There is sufficient evidence that African cacti are taller on average.The null hypothesis is not rejected. There is sufficient evidence that African cacti are taller on average.    The null hypothesis is not rejected. There is insufficient evidence that African cacti are taller on average.The null hypothesis is rejected. There is insufficient evidence that African cacti are taller on average.

(e) Explain the type of error, in context, that might have been made.

Type II error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.    Type I error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.Type II error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.

(f) What would the p-value have been if we had done a two-tailed test? (3 decimal places)

. Average coffee consumption among graduate students is commonly known to be 3.89 cups per day. A graduate student took a sample of 10 fellow graduate students in her statistics class, and in the sample produced a mean of 4.02 cups per day and a standard deviation of .19. Because of this, she believes that the average is actually greater than what is commonly thought (3.89 cups per day). Do we believe the graduate student’s claim or the common belief? Use a significance level of .01. Show all the steps (4 steps)

Use a 5% significance level.

In a large city,  200  persons were selected at random and each person was asked how many tickets he purchased that week in the state lottery. The results are given in the following table. Suppose that among the  7  persons who had purchased  five  or more tickets,  3  persons had purchased exactly five tickets,  2  persons had purchased six tickets,  1  had purchased seven tickets, and  1  had purchased ten tickets. Test the hypothesis that these  200  observations form a random sample from a  Poisson distribution.                                                                                                      

NOTE !!! : COULD YOU PLEASE ANSWER IT USING MINITAB (also with the steps(procedure) you click in minitab)

Is there a relationship between incubation period and hospitalization period? Comment using graphs and statistical proofs by calculating the correlation coefficient.

Is there a relationship between total infection period vs. age and market encounter of patients? Comment using graphs and statistical proofs. What is the relationship equation and how much of the variation is explained by the model?

Use 5% level of significance. At the fifth hockey game of the season at a certain arena, 200 people were selected at random and asked as to how many of the previous four games they had attended. The results are given in the table below.

Test the hypothesis that these  200  observed values can be regarded as a random sample from a  binomial distribution,where  ‘θ’  is the unknown parameter representing the probability of success that a person will attend a game.

Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. We obtain the following data for 9 glasses of water. Each glass contained the same amount of water. We look at the zinc concentration (mg/L) in bottom water and the zinc concentration in surface water for each glass. It is fine to round any standard deviations to 2 decimals.

Glass 1 2 3 4 5 6 7 8 9

Bottom Water .48 .32 .62 .58 .76 .77 .70 .64 .52

Surface Water .42 .24 .39 .41 .61 .61 .63 .52 .41

Use a 96% confidence interval. Assume that the differences follow a normal distribution.

When I sit and watch my students take exams, I often think to myself "I wonder if students with bright calculators are impacted by the pretty colors." This leads me to wonder if there is a difference in the exam scores of students with colorful calculators versus the exam scores of students with plain black calculators. To investigate further, I took a sample of past students. There were 49 students with colorful calculators with a mean exam score of 84 and a corresponding standard deviation of 4.7. There were 38 students with plain black calculators with a mean exam score of 87 and a corresponding standard deviation of 5.7. Is there sufficient evidence to suggest the mean exam scores of my STA 215 students with colorful calculators are different than the mean scores of my STA 215 students with plain black calculators?

(Calculate the difference as Black - Colorful.)

What is the value of the test statistic, and what is the p value for that test statistic? Give your answer to 2 decimal places.

Garcia's Grill offers 8 side dishes, 4 types of steak, and 5 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 2 different toppings and 4 different side dishes?