1. What is a p-value and how is it used to make a decision about the null hypothesis?
2. How is the p-value related to the test statistic?
3. Explain whether or not rejecting the null hypothesis makes the alternative hypothesis true and why.
4. If I conduct a hypothesis testing with Type I error set at 0.05 and a resulting p-value of 0.3, what would my conclusion be?

Calculate several samples of the unit impulse and impulse responses of y(n) = -0.75 y(n–1) + x(n) – 0.3 x(n–1) – 0.4 x(n-2).

Re-write the equation in standard form and then indicate the name of each coefficient (a₁, etc.). Use the filter() function in MATLAB to check your results to 1 and 2.

Follow the decay of parent 87Rb and growth of daughter 87Sr in a granite sample over the course of six half-lives. Assume that the granite initially contains 1.2 x 10^20 atoms of 87Rb and 0.3 x 10^20 atoms of 87Sr. The half-life of 87Rb is 48.8x10^9 years. Show the results graphically on the graph paper below.

Carbon monoxide emissions for a particular car vary with an average of 2.5 g/mi and a standard deviation of 0.3 g/mi. A company has 60 of these cars in its fleet. If X= the CO level for the company's fleet, what is the probability that the average of the 60 cars falls between 2.55 and 2.6 g/mi? Round your answer to four decimal places .

1. A company manufactures concrete blocks for construction purposes. We know that the weights of the individual concrete blocks are normally distributed with a mean value of 11 kg, and a standard deviation of 0.3 kg.

1. The company can be 99% confident that the any randomly selected concrete block has a weight within the interval
2. The probability that a concrete block weighs less than 10.5 kg is

The commute time X each working day has the mean of 1 hour and standard deviation of 0.3 hours.

(1) What is the approximate distribution of the average daily commute time for a period of 36 days, by the Central limit theorem? Include the parameters.

(2) Find the probability that the average daily commute time for this period is larger than 1.06 hours.

Question 3

Suppose that X and Y have the following joint probability distribution:

Find the followings:

1. E(Y)=
2. Var(X)=
3. Cov(X,Y)=
4. Correlation(X,Y)=

A radioactive mass emits particles according to a Poisson process at a mean rate of 2.5 per second. Let T be the waiting time, in seconds, between emissions.

1-What is the median waiting time?

2-Find P(0.3 < T < 1.5).

3-If 3 seconds have elapsed with no emission, what is the probability that there will be an emission within the next second

The mass-spring-damper system has a 2 kg block is displaced by an amplitude of 50 mm and
released. Ifthc phase angle ofrcsponse is 84.17o, how many cycles (m) will be executed beforc
the amplitude is reduced to I mm. What are the undamped natural frequency m« and spring
constant k ifthc period ofdamped oscillation rs is 0.3 scc.

1. What is a p-value and how is it used to make a decision about the null hypothesis?
2. How is the p-value related to the test statistic?
3. Explain whether or not rejecting the null hypothesis makes the alternative hypothesis true and why.
4. If I conduct a hypothesis testing with Type I error set at 0.05 and a resulting p-value of 0.3, what would my conclusion be?