An automobile manufacturer claims that its cars average more than 410 miles per tankful (mpt).
As evidence, they cite an experiment in which 17 cars were driven for one tankful each and
averaged 420 mpt. Assume σ = 14 is known.

a. Is the claim valid? Test at the 5 percent level of significance.

b. How high could they have claimed the mpt to be? That is, based on this experiment, what is the maximum value for µ which would have been rejected as an hypothesized value?

c. What is the power of the test in part (a) when the true value of µ is 420 mpt? (Hint: Your rejection region for part (a) was stated in terms of comparing Zobs with a cut-off point on the Z distribution. Find the corresponding x̅cut-off and restate your rejection region in
terms of comparing the observed x̅value with the x̅cut-off. Then assume H1 is true (i.e. µ
= 420 mpt) and find the probability that x̅is in the rejection region.)

An automobile manufacturer claims that its van has a 38.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 240 vans, they found a mean MPG of 38.1. Assume the standard deviation is known to be 2.0. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Enter the value of the test statistic.

You are driving along straight road. You cover 200 miles in 4 hours? Does that mean that your speedometer read 50 mph for your entire trip? Is is necessary that your speedometer register 50 mph at least once during the trip? Use math to explain your answer.

I understand that your speedometer would not be 50mph for the entire trip, but I am not sure how to explain it using math.

You are testing a treatment for a new virus. Effectiveness is judged by the percent reduction in symptoms after two weeks.It is known that if left untreated, symptoms will reduce on their own by 0.185 (18.5%) with a standard deviation of 0.123. Three trials were run simultaneously.Trial 1 involved giving the participants a sugar pill. Patients in Trial 2 were given Agent A. Patients in Trial 3 were given Agent B. Results showing the amount of symptom reduction for the various trials are summarized in the table to the left. Note that this is NOT a paired t-test.Patient 1 just means the first patient to be given the treatment in each trial. Patient 1 is a different person in each trial.

1) At the 80%, 90% and 95% confidence levels (alpha = 0.2, 0.1 and 0.05) compare Agent A, Agent B and the Sugar Pill results to the population symptom reduction. Use a one-tail hypothesis test.

5. (a) What type of post-translational modification direct protein for proteasome degradation? (0.3 pt)

(b) Which amino acid residue on the protein does the modification occur? What is the functional group that modify the protein? What types of bonds link the protein and modification group together? (0.6 pt)

(c) Describe the three functions of the 19S subunit of proteasome (0.6 pt).

(d) Describe the function of the 20S subunit of proteasome (0.2 pt).

Calculating the variance and standard deviation: Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return and the standard deviation of the return on Barbara’s investment.

Suppose that the USDA expects that 53.3 billion bushels of soybeans will be produced this year at a price of $8.50/bushel. Assume that the elasticity of supply is 0.3 and that the elasticity of demand is -0.2 (both very inelastic).

1. Derive the linear supply and demand curves for this equilibrium.

2. What quota is required to increase the soybean price to $9.25/bushel? And what is the economic cost of this solution (i.e., what is the change in producer surplus and change in consumer surplus, and what is the sum of these changes)?

How to create a compacted data set by combining the columns Old, Older, Young, Younger and place them in into one single new column called age using python pandas.

Consider an i.i.d. random sample of size 3 denoted by ?1,?2, ?3 from the same population, where the mean ? and variance ? 2 are unknown. Suppose that you have the following two different estimators for mean ?. (Remember: no work, no credit.) ?̂1 = 0.3?1 + 0.5?2 + 0.2?3 ?̂2 = 0.5?1 + 0.5?3 a. Is ?̂1 unbiased? b. Is ?̂2 unbiased? c. Which one is preferred, ?̂1 or ?̂2?

(a) The price elasticity of demand for smoke grinders in response to changes in the price of purpletts is -2. What formula and concept will we use to study the change in quantity demanded of smoke grinders to a change in price of purpletts? What the -2 elasticity of demand tells us about the goods purpletts and smoke grinders? (b) Given the table below, answer the following question. The quantity demanded of which good decreases the most during a recession (when incomes decrease)?

Given the table below ( income elasticity of demand), answer the following question.

Total brand cereal = 0.3, eclipse galsses = -1.5, office chairs = 0, theater tickets = 4, heart shaped pillows = 2

The quantity demanded of which good decreases the most during a recession (when incomes decrease)?