Researchers wanted to compare the GRE scores of the students who were trained in an academy and the students who didn't receive any training. One group of 80 students, who had the training, had a mean score of 315. Another group of 120students, who had no training, had a mean score of 305. Assume the population standard deviations for the scores for the students who take the training and the students who don't take the training are 25 and 20, respectively. Find the lower bound of the 95% confidence interval for the difference in population scores between students who had the training and students who didn't have the training. Let the students who had the training be the first sample and let the students who didn't have the training be the second sample. Assume that both the population distributions are normally distributed. Assume the samples are random and independent. Round your answer to two decimal places.

School is interested in knowing the average height of undergraduate students but do not have time to measure all the students. 100 students were randomly selected and it is found that the average height of these 100 students is 1.60 metres with a standard deviation of 0.3 metres.

a) State the point estimate of the average height of undergraduate students.

b) Construct an interval estimate of the average height of students with 99% confidence.

c) The respond rate of the above survey was 85%, i.e. 85% of the students contacted were willing to participate in the survey. Construct an interval estimate of the proportion of students population who are willing to participate in other similar survey with 95% confidence.

d) The Student Services Centre is not very convinced of the result and would like to conduct a second survey. It would like to estimate the mean population height of students to be within 0.05 metres and be 99% confident, assuming the population standard deviation is 0.3 metres, how large a sample is necessary to achieve the accuracy stated?

Scientific Name: Vitis aestivalis × V. riparia = V. ×slavinii Common Name: Slavin’s grape

can anyone give a description of this plant, along with leaf shape, flowers, etc.

Let t be a positive integer. Prove that, if there exists a Steiner triple system of index 1 having v varieties, then there exists a Steiner triple system having v^t varieties

Is the following equation dimensionally correct?

v= sqrt(pH/PE)

v= feet per second

p = grams per cubic cm

H = height in feet

PE = joules

Create your own 2 × 2 payoff matrix for a two-person zero-sum game with v − < v+. Solve your game (find a saddle point and the value of the game).

(Relativity) Draw the world line of a particle moving in the XY plane:

a) Describing a circle with constant speed V

b) Accelerating from the rest until reaching certain speed V

Complete the proof for the claim that any open ball B(x₀,r) in Euclidean space Rⁿ is homeomorphic to Rⁿ.

proof is given below the theorem. Show that suggested map g is in fact homeomorphism.

Theorem: Let X₀, X₁, and X₂ be topological spaces and let f: X₀ -> X₁ and g : X₁ -> X₂ be continuous functions. Then g∘f : X₀ -> X₂ is continuous.

proof : Suppose that V is open in X₂. Since g is continuous, g^-1(V) is open in X₁. Since f is continuous, f^-1(g^-1(V)) = (g∘f)^-1(V) is open in X₀. It follows that g∘f is continuous.

Let V = R4 and let U = hu1, u2i, where u1 =    1 2 0 −3    , u2 =     1 −1 1 0    . 1. Determine dimU and dimV/U. 2. Let v1 =    1 0 0 −3    , v2 =     1 2 0 0    , v3 =     1 3 −1 −6    , v4 =     −2 2 0 9    . For any two of the vectors v1,...,v4, determine whether they are in the same coset of U in V or not. 3. Find a basis of V that contains a basis of U. Hence, determine a basis of V/U. 4. Find two (distinct) elements of the coset e1 + U.

Drag measurements were taken for a 5 cm diameter sphere in water at 20 °C to predict the drag force of a 1 m diameter balloon rising in air with standard temperature and pressure. Given kinematic viscosity of water (v) = 1.0 X 10^-6 m²/s and kinematic viscosity of air (v) = 1.46 X 10^-5 m²/s.

1. Perform the Buckingham Pi theorem to generate a relationship for F_D as a function of the independent variables. Assume the drag F_D is a function of diameter (d), velocity (V), fluid density (ρ) and kinematic viscosity (v)

2.Determine the sphere velocity if the balloon was rising at 3 m/s