A researcher conducts a study of white and black attitudes toward the police in his state.

The percentage of a random sample of white respondents (N = 300) who say they have a favorable attitude toward the police is 61%. The percentage of a random sample of black respondents (N = 250) who say they have a favorable attitude toward the police is 47%.

• Is there a real (statistically significant) difference between the percentage of Whites and African Americans who have a positive attitude toward the police in the larger population, or are these results likely to have occurred by chance?
• Construct a 95% confidence interval for the proportion of Whites in the population who have a favorable attitude toward the police.
• Construct a 95% confidence interval for the proportion of African Americans in the population who have a favorable attitude toward the police.

Please show work. I want to learn how to execute the question. Class does not use any statistical softwares or excel.

In a survey of smokers who tried to quit smoking with the nicotine patch therapy, 39 were smoking one year after treatment and 32 were not smoking one year after treatment. We want to use a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch therapy the majority are smoking one year after treatment..

What is the p-value if the claim is modified to state that if the proportion is equal to 0.05?

Whenever you are asked to test a hypothesis, be sure to: (a) state the null and alternative hypotheses; (b) state the relevant sample statistic; (c) give the rejection region; (d) compute the test; (e) give your decision and a conclusion in English.

1. Assume that last year, licensed American drivers drove an average of 10,000 miles, with a standard deviation of 2,000 miles (these are population figures). This year, the government campaigned to get people to save gas by driving less. To test the effectiveness of the campaign, a study is conducted. A sample of 100 drivers is drawn at random from the general population and the number o fmiles driven by each person is recorded. On the average, these 100 drivers drove 11,000 miles. Was the campaign effective? Use alpha = .01.

Use Excel/Megastat to find the discrete probability and cumulative probability of the Binomial distribution with probability of success p = 0.3 and n = 70.

Find its mean and variance.

Based upon the chart on Excel, what can you conclude about the binomial convergence?

Use binom.dist function on Excel and sketch the curve.

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April , ). Assume that room rates are normally distributed with a standard deviation of $55.

a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)?

b. What is the probability that a hotel room costs less than $140 per night (to 4 decimals)?

c. What is the probability that a hotel room costs between $200 and $300 per night (to 4 decimals)?

d. What is the cost of the 20% most expensive hotel rooms in New York City? Round up to the next dollar.

A baseball team's 40-man roster contains 21 pitchers, 4 catchers, 9 infielders, and 6 outfielders. If a player from this roster is selected randomly, what is the probability that he is an infielder or outfielder?

The Mozart Effect pertains to the hypothesis that listening to Mozart might induce a short-term improvement on the performance of certain kinds of mental tasks. A team of researchers were interested in seeing if this would apply to a general intelligence test. They do not know if this will improve or lower scores for this particular task but they collected data from two groups:

a. Treating these two groups as independent, answer the following:
* State the hypotheses for this analysis and if this is a one- or two-tailed test.
* State your alpha value and the critical values.
* Test this hypothesis (showing your calculations).
* State your decision regarding the null hypothesis.

b. Now, conduct those four steps again but treat these two groups as dependent (e.g., each row now belongs to the same person in a repeated-measures design).

c. Do the two tests lead to different conclusions? Comment on why or why not.

Consider a population proportion p = 0.88.

a-1. Calculate the expected value and the standard error of P−P− with n = 30. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.)

b-1. Calculate the expected value and the standard error of P−P− with n = 60. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.)  

To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded.

Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? (b) Use a 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as "impaired minus normal." State the appropriate conclusion.

Subject Normal,Xi Impaired, Yi

1 4.49 5.86

2 4.24 5.67

3 4.58 5.51

4 4.56 5.29

5 4.31 5.90

6 4.80 5.49

7 4.59 5.23

8 5.00 5.61

9 4.79 5.63

A machine in the math lab dispenses coffee. The average cup of coffee is supposed to contain 7 oz. Eight cups of coffee from this machine show the average content to be 7.3 oz. The population standard deviation is 0.5 oz. Do you think the machine has slipped out of adjustment and the average amount of coffee per cup is different from 7 oz? Use a 5% level of significance.

1. stating the null and alternate hypothesis

2. find the p value

3. make your decision to reject or fail to reject the null hypotheses

4. write your conclusion to the problem.

5.  Use the results from above, find a 0.95 confidence interval for the mean number of cups of coffee.

6. Explain in a sentence what the results in #5 mean.

Shown below is a portion of a computer output for a regression analysing relating Y(dependent variable) and X(independent variable)

ANOVA

df SS

Regression    1    115.064

Residual 13    82.936

Coefficient    Standard error

Intercept 15.532    1.457

X -1.106 0.761

Required :- A) Perform a t test using the p value approach and determine whether x and y are related Let alpha=0.5 . B) Using the p value approach, perform an F test and determine whether x and y are related. C) Compute the coefficient of determination and fully interpret its meaning. Be specific.

Suppose a coin is biased. Specifically, the probability that the flip shows as heads is a random variable P with the probability density function f P(p) = 2(1−p) for 0 ≤ p ≤ 1. Let N be the number of heads in n independent flips of the coin. Find E [ N ] using iterated expectation.

(6.29 & 6.67) Strategic placement of lobster traps is one of the keys for a successful lobster fisherman. An observations study of teams fishing for the red spiny lobster in Baja Cali- fornia Sur, Mexico, was conducted and the results published in Bulletin of Marine Science (April 2010). One of the variables of interest was the average distance separating traps - called trap spacing - deployed by the same team of fishermen. Consider the trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen: 93, 99, 105, 94, 82, 70, 86. Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico.

a. Identify the target parameter for this study.

b. Compute a point estimate of the target parameter.

c. What is the problem with using the standard normal statistic to find a confidence interval for the target parameter?

d. Find a 95% confidence interval for the target parameter.

e. Give a practical interpretation of the interval in part above.

f. What conditions must be satisfied for the interval in part (d) to be valid?

The lifetime of lightbulbs that are advertised to last for 3900 hours are normally distributed with a mean of 4100 hours and a standard deviation of 300 hours. What is the probability that a bulb lasts longer than the advertised figure?

or Exercises 5 through 20, assume that all variables are approximately normally distributed. Stress Test Results For a group of 12 men subjected to a stress test situation, the average heart rate was 109 beats per minute. The standard deviation was 4. Find the 99% confidence interval of the population mean.