Crude oil of specific gravity (0.75) is flowing through a pipe. The pipe has a diameter of 100 mm and 50 mm at the sections 1 and 2 respectively. The velocity of crude oil at the section 1 is 550 cm/s. The   section 1 is 3000 mm and section 2 is 2000 mm above the datum. If the pressure at the section 1 is 0.2 N/mm², find the intensity of pressure at section 2?

In Java, write the method public static void insertUnique(List l, T e), user of the ADT List. The method takes a list l and an element e and inserts the element at the end of the list only if it is not already there. Example 0.2. If l : A → B → C, then after calling insertUnique(l, "C"), the list does not change. Calling insertUnique(l, "D") will make l be : A → B → C → D.

1.

During the first 13 weeks of the television season, the Saturday evening 8:00 P.M. to 9:00 P.M. audience proportions were recorded as ABC 30%, CBS 27%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 93 homes, CBS 63 homes, NBC 88 homes, and independents 56 homes. Test with  = .05 to determine whether the viewing audience proportions changed. Use Table 12.4.

Round your answers to two decimal places.

χ ² = ??

2.

Test the following hypotheses by using the χ ² goodness of fit test.

A sample of size 200 yielded 40 in category A, 120 in category B, and 40 in category C. Use  = .01 and test to see whether the proportions are as stated in H₀. Use Table 12.4.

a. Use the p-value approach.

χ ² = ?

The table below contains the following variables, growth rates of real GDP, M1, M2, velocity of M1 and M2 (denoted V1 and V2), the federal funds rate (FFR), and the CPI inflation rate. Use the quantity equation to calculate the equilibrium inflation rate using individually M1 and M2. Next, calculate the equilibrium inflation rate assuming the quantity theory of money holds (i.e. assuming velocity is constant). According to your calculations, which is a better predictor of inflation, M1 or M2? Similarly, which is a better predictor of inflation, assuming the quantity theory holds, or not?

Table 8.3: Growth Rates

(Source: FRED II, St. Louis Federal Reserve)

A stress researcher is measuring how fast parents respond to a crying infant. He gathers data from 64 people (N = 64). His participants' reaction times are normally distributed. The average reaction time was 3.0 seconds, with a standard deviation of 0.2 seconds. Using a standard normal table (Table A-1), answer the following questions (hint: you need to convert raw scores into z-scores).

a. What proportion of his participants will be between 2.6 and 3.1 seconds?
b.      What proportion of his participants will be between 2.4 and 3.2?
c. What proportion of his participants will be between 3.3 and 3.7?
d. What proportions of participants will be above 3.4 seconds?
e. Of the z-scores you calculated above which is the most probable? Which is the least probable? Explain your answers.
f. What would the standard error of the mean be for the sampling distribution from which this sample of reaction times was drawn, if we assume the population SD (sigma, σ) is also 0.2?
g. If we are using an alpha = .05, what would the critical values be in raw units (hint: you don't need the z-table for this)?

An economist wondered if people who go grocery shopping on weekdays go more or less often on Fridays than any other day. She figured that if it were truly random, 20% of these shoppers would go grocery shopping on Fridays. She randomly sampled 75 consumers who go grocery shopping on weekdays and asked them on which day they shop most frequently. Of those sampled, 24 indicated that they shop on Fridays more often than other days.

The economist conducts a one-proportion hypothesis test at the 1% significance level, to test whether the true proportion of weekday grocery shoppers who go most frequently on Fridays is different from 20%.

(a) H0:p=0.2; Ha:p≠0.2, which is a two-tailed test.

(b) Use Excel to test whether the true proportion of weekday grocery shoppers who go most frequently on Fridays is different from 20%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

Provide your answer below:

test statistic =    p-value =

A paddle ball toy consists of a flat wooden paddle and a small rubber ball that are attached to each other by an elastic band (figure). You have a paddle ball toy for which the mass of the ball is 0.014 kg, the stiffness of the elastic band is 0.890 N/m, and the relaxed length of the elastic band is 0.325 m. You are holding the paddle so the ball hangs suspended under it, when your cat comes along and bats the ball around, setting it in motion. At a particular instant the momentum of the ball is <−0.02, −0.01, −0.02 > kg·m/s, and the moving ball is at location <−0.2, −0.61, 0> m relative to an origin located at the point where the elastic band is attached to the paddle.

(a) Determine the position of the ball 0.1 s later, using a Δ⁢t of 0.1 s. (Express your answer in vector form.)

(b) Starting with the same initial position (<−0.2, −0.61, 0> m) and momentum (<−0.02, −0.01, −0.02 > kg·m/s) determine the position of the ball 0.1 s later, using a Δ⁢t of 0.05 s. (Express your answer in vector form.)

(c) If your answers are different, explain why.

• Assume, as in the example in the book, that the job separation rate s is 0.01 (1%)

  per month and that the job finding rate f is 0.2 (20%) per month.

• Assume that the labor force is 100 million.

  (a) What is the steady state unemployment rate for this economy?

  (b) Given that L = 100 million, what is the steady state number of employed E and unemployed U ?

(c) If U.S. immigration policy changed today (period t = 1) such that we allowed more people to enter the country and L increased to 110 million from its initial value of 100 million. Assume that these new entrants would be unemployed first and then find jobs at the job finding rate f . Create a table (maybe in Excel) that shows how E, U , and U/L evolve over time, givens = 0.01 and f = 0.2, starting at t = 1 and ending when the unemployment rate reaches its steady state rounded to the nearest thousandth.

(d) In the table from the previous scenario, how many periods does it take for the unemployment rate to reach its steady state level rounded to the nearest thousandth?

The sugar content of the syrup in canned peaches is normally distributed. Suppose that the variance is thought to be σ^2=18⁢  (milligrams)^2. A random sample of n = 10 cans yields a sample standard deviation of s = 4.8 milligrams.

(a) Test the hypothesis H0:σ^2 = 18 versus H1:σ2 ≠ 18 using α = 0.05
Find χ02 .Round your answer to two decimal places (e.g. 98.76).

Is it possible to reject H0 hypothesis at the 0.05 level of significance?

A. Yes

B. No

Find the P-value for this test.

(b) Suppose that the actual standard deviation is twice as large as the hypothesized value. What is the probability that this difference will be detected by the test described in part (a)?

(c) Suppose that the true variance is σ2=40. How large a sample would be required to detect this difference with probability at least 0.90?