An extensive study conducted in 1980 concluded that the mean mercury level in oysters from the White Bear estuary was .021 ppm with a standard deviation of .031. in 2012 a sample of 41 oysters from the same estuary exhibited a mean mercury concentration of .007 ppm. Can you conclude that the 2012 mercury concentration is lower than in 1980? Use a=.01 level of significance. Use P-Value test.

Hypothesis with claim

TV

PV

Decision and explanation

Summary

A researcher hypothesizes college students will be more extroverted than the population mean for extroversion and collects n = 177 students. The researcher performs a one-tail z test with alpha set to 0.05 and finds a sample z score is 2.44, showing evidence for the researcher's predictions. What is the probability (as % or proportion) the researcher made a type 1 error?

b. A researcher hypothesizes that coffee drinkers and non coffee drinkers will have different incidences of clinical anxiety. The researcher finds that those who drink more coffee are more likely to be anxious. Is this research a one tail or two tail test?

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A golf equipment manufacturer would like to convince members of a club that its golf balls travel farther than those of a rival. For the comparison, twelve golfers were randomly selected from the club to each drive a ball from this manufacturer and from the rival. The results show the distance traveled, in yards. The complete set of results is provided below:

Should every golfer hit the rival ball first and then the manufacturer’s ball second? Explain your answer.

State the null hypotheses, paste the test output, and state your decision.

What is the 95% confidence interval for the mean difference? Interpret the confidence interval.

What assumption(s) was (were) required to perform this hypothesis test?

Does (do) the assumption(s) appear to be reasonably met in this case? Paste the Minitab output required to answer this question here.

Comment on the source of sampling error and a potential source of non-sampling error for this study (be specific).

Rather than have each golfer hit one ball of each type, the manufacturer could have easily chosen 12 more golfers and allowed all 24 golfers to hit one ball. Should the manufacturer run the study as it did (12 golfers hitting each type of ball) or with 24 golfers hitting just one randomly assigned ball? Justify your answer.

The complete set of results is provided below:

33. a. What z score cuts off the bottom 2.5% of all scores in the normal distribution?

b.  If shoe size in humans has a mean of µx = 10.4 and a standard deviation of σx = 1.8, and Rodney has a shoe size of 8.9, what proportion of humans have shoes larger than Rodney?

c.  What happens to the standard error of x̅ as sample size increases?

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Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 11.2 minutes and a standard deviation of 2.1 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 7 and 13 minutes

(b) the response time is less than 7 minutes

(c) the response time is more than 13 minutes

Consider the following variant of two-finger morra, where Alice picks an action a ∈ {1, 2} and Bob picks an action b ∈ {1, 2}. Bob pays Alice $(a × b) if a + b is even, and Alice pays Bob $(a × b) if a + b is odd. Note that the payoff is different than that in the example we used in class.

1) If Alice plays 1 finger with probability p and 2 fingers with probability 1 − p, what’s the expected payoff that Bob can achieve if he knows p? How should Alice choose p such that Bob’s payoff is indifferent of his own choices?

2) If Bob plays 1 finger with probability q and 2 fingers with probability 1 − q, what’s the expected payoff that Alice can achieve if she knows q? How should Bob choose q such that Alice’s payoff is indifferent of her own choices?

3) What is the Nash equilibrium strategy for both players? And what is the expected payoff for each if they play the Nash equilibrium strategy?

A shipyard makes a container ship that can withstand the total amount of weight W, which is normally distributed with mean of 600 tons and standard deviation of 60 tons. Let us assume that the weight of a single container that will be loaded to the container ship is also normally distributed with mean of 4 tons and standard deviation of 0.4 tons. What is the maximum number of containers that the ship can load and still have at least a 90% chance to not exceed its weight limit? Your answer has to be an integer

You roll two six-sided even dice. What is the probability that you get a score of at least 11?

a. 2/11

b. 1/12

c. 1/18

d. 1/6 
 


You toss a fair coin 3 times in a row. What is the probability of getting at most two heads?

a. 3/4

b. 1/4

c. 3/8

d. 7/8

a) A bank is interested in studying the number of people who use the ATM. On average, 2 customers walk up to the ATM during any 10 minute. Find the probability in each case.

i) Atleast 5 customer in 20 minutes.

ii) Fewer than 6 but more than 2 customer in 10 minutes.

b) Anderson Research is a full-service marketing research consulting firm. Recently it was retained to do a project for a major U.S. airline. The airline was considering changing from an assignedseating reservation system to one in which fliers would be able to take any seat they wished on a first-come, first-served basis. The airline believes that 70% of its fliers would like this change if it was accompanied with a reduction in ticket prices. Anderson Research will survey a large number of customers on this issue, but prior to conducting the full research, it has selected a random sample of 20 customers. Find the probability in each case:

i) Atleast 12 like the proposed change

b) More than 9 but less than 16 like the proposed change.

Out of 300 people sampled, 249 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to three places

The weights of American newborn babies are normally distributed with a mean of 119.54 oz ( about 7 pounds 8 ounces) and a population standard deviation of .61 oz. A sample of 11 newborn babies is randomly selected from the population.

(a) find the standard error of the sampling distribution. Round your answer to 4 decimal places.

(b) Using your answer to part (a), what is the probability that in a random sample of 11 newborn babies, the mean weight is at most 119.39 oz? Round your answer to 4 decimal places.

(c) using your answer to part (a), what is the probability that the random sample of 11 newborn babies, the mean weight is more than 120.03 oz? round your answer to 4 decimal places.

It has been observed that some persons who suffer colitis, again suffer colitis within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 114 people in the first group and this group will be administered the new drug. There are 165 people in the second group and this group wil be administered a placebo. After one year, 19% of the first group has a second episode and 21% of the second group has a second episode. Select a 99% confidence interval for the difference in true proportion of the two groups.

a) [−0.170, 0.130]

b) [−0.645, 0.605]

c) [−0.130, 0.170]

d) [−0.105, 0.022]

e) [−0.145, 0.105]

f) None of the above

Based on past trends, we have enough reason to believe that 60% of Ha Cafe customers prefer rice and 40% prefer vermicelli. A sample of 5 customers is to be selected. The probability that fewer than 2 prefer rice is

9. The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter r is used at a rate of 6%.

a. Find the mean and standard deviation for the number of times the letter r will be found on a typical page of 2600 characters. (1 dp)

b. In an intercepted ciphered message sent to Iran, a page of 2600 characters is found to have the letter r occurring 178 times. Is this unusually low or high?