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"A famous American football coach had only two strategies, Run the ball to the left side of the line and Run the ball to the right side. The defense can concentrate forces on the left side or the right side. If the opponent concentrates on the wrong side, his offense is sure to gain at least 5 yards. If the defense defended the left side and the offense ran left, the offense gained only 1 yard. If the opponent defended the right side when the offense ran right, the offense would still gain at least 5 yards with probability 0.50. It is the last play of the game and the famous coach's team is on offense. If it makes 5 yards or more, it wins; if not, it loses. Both sides choose Nash equilibrium strategies.
Is there a Nash equilibrium in pure strategies in this game? Explain why or why not.What is the probability that the offense will run to the left?What is the probability that the offense will run to the right?What is the probability that the defense defends the left hand side?What is the probability that the defense defends the right hand side?Explain in words what the expected outcome will be.
In the new poll, if the proportion favoring the incumbent has not changed, what is the mean and standard deviation of the number preferring the incumbent?
A random sample of 36 drinks from a soft drink machine has an average content 7.6 ounces with an standard deviation of 0.48 ounces. Test the hypothesis ounces against the alternative hypothesis at the 0.05 level of significance.
Outline the difference between the t test for independent groups and the t test for matched groups. A researcher computed the F ratio for a four-group experiment.The computed F is 4.86. The degrees of freedom are 3 for the numerator and 16 for the ..
A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples
Illustrate by computation that, for straight -line regression of Y on x, β1= 0.
Estimate the true proportion of college students who believe in the possibilty of haunted places with 99% confidence.
A population is Normally distributed and has a σ =24. Samples of size 25 have a sample mean of 100. Find the 90% confidence interval for the population mean.
You are appraising the quality of diamonds for your importer. A diamond without a clear center (opaque center) shall be downgraded and sold at discount.
The mean number of flaws per 100 m of material produced on a certain machine at Blanktown Fabrics is 2. If flaws occur randomly, find the probability that in 50 m of material there will be less than 2 flaws.
Find the β risk and power assuming that the true mean is really 380 square feet per gallon. (b) Construct a left-sided power curve, using increments of 5 square feet (400, 395).
Why is effective sampling important when performing a hypothesis test? What could happen if your sample is not appropriate to your study?
Convert the height of the stack of pennies into meters. Calculate how many pennies would be needed to make a tower 1 billion meters tall. Give answer in both standard calculation and in scientific notation.
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