A random sample of 64 drivers used on average 747 gallons of gasoline per year. The standard deviation of the population is 34 gallons.

Find the 99% confidence interval of the mean for all drivers. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.

A random sample of 19 rainbow trout caught at Brainard lake, Colorado, had mean length x = 11.9 inches with sample standard deviation o 2.8 inches.
Find a 95% confidence interval for the population mean length of all rainbow trout in this lake.
b. interpret the meaning of the confidence interval in the context of this problem .

A random sample of 78 students was interviewed, and 59 students said that they would vote for Jennifer James as student body president.
a. Let p represent the proportion of all students at this college who will vote for Jennifer. Find a point estimate p for p.
b. Find a 98% confidence interval for p.

A random sample of 25 employees of a local utility firm showed that their monthly incomes had a sample standard deviation of $112. Provide a 90% confidence interval estimate for the standard deviation of the incomes for all the firm's employees.

Background: Anorexia is well known to be difficult to treat. The data set provided below contains data on the weight gain for three groups of young female anorexia patients. These groups include a control group, a group receiving cognitive behavioral therapy and a group receiving family therapy. Source: Hand, D. J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. eds (1993) A Handbook of Small Data Sets. Chapman & Hall, Data set 285 (p. 229).

Directions: Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it. Then perform an analysis of variance (ANOVA) to determine whether or not the differences in weight gain between the treatment groups is statistically significant.

Data

1. State the null and alternative hypotheses.
   
   
   
2. Compute the test statistic. Document how SSTr and SSE were computed. Use 4 decimal places for the sample means, sample standard deviations and the grand mean and round your answers for SSTr and SSE to 2 decimal places

   Use the values for SSTr and SSE to complete the following ANOVA table. Round each of your answers to 2 decimal places.

   Source	S.S.	df	M.S.	F
   Treatment
   Error
   Total

3. Compute the p-value. Provide the name of the distribution and the parameters used to compute the p-value. Then enter your answer rounded to 4 decimal places.
   
   
   
4. Interpret the results of the significance test. Is this result statistically significant? Is this result important from a practical perspective?
   

A jar contains 2 green marbles, G1 and G2, and 4 yellow marbles, Y1, Y2, Y3, and Y4. Imagine that we do not know this. Suppose that our parameter p of interest is the proportion of marbles in the jar that are green. We will be allowed to take three marbles out the jar (all at once, without replacement). We will estimate p by looking at ˆp, the proportion of marbles in our sample that are green.

(a) Write down the sampling distribution of ˆp, showing enough work that I can follow. (Assuming that pˆ is approximately normal is not valid in this case [why?] so don’t do it.)

(b) Is ˆp an unbiased estimator for p? Answer clearly and then explain, showing all necessary work.

Imagine that proportion p = 0.82 of adults in a large city are married, but that this is not known, and we would like to estimate p. Suppose that we survey a random sample of 250 adults in the city, and calculate ˆp, the sample proportion of respondents who are married.

(a) Are the requirements met for ˆp to be approximately normally distributed? Explain, showing any necessary calculations and/or computer commands.

(b) What is (approximately) the probability that ˆp will fall between 0.81 and 0.83? Show all calculations and/or computer commands.

(c) If we had sampled only 50 adults, would the requirements for ˆp to be approximately normal still hold? Explain.

Problem 1 This problem will present the same scenario two different ways – the second one will add an additional piece of information. For each scenario, you will construct an influence diagram, as indicated in the problem. (a) Imagine that a close friend has been diagnosed with heart disease. The physician recommends bypass surgery. The surgery should solve the problem. When asked about the risks, the physician replies that a few individuals die during the operation, but most recover and the surgery is a complete success. Thus, your friend can (most likely) anticipate a longer and healthier life after the surgery. Without surgery, your friend will have a shorter and gradually deteriorating life. Assumingthat your friend’s objective is to maximize the quality of her life, construct an influence diagram for this scenario.(b) Suppose now that your friend obtains a second opinion. The second physician suggests that there is a third possible outcome: Complications from surgery can develop which will require long and painful treatment. If this happens, the eventual outcome can be either a full recovery, partial recovery (restricted to a wheelchair until death) or death within a few months. Draw the influence diagram that represents the situation after hearing from both physicians. How does this change the influence diagram that you created in part (a)?

What are the other names that omitted variable bias is called?

Why is regression analysis necessary in business? What two categories of regression models are used? Explain

5.Pashley Package Holidays has to decide whether to discount its holidays to destinations abroad next summer in response to poor consumer confidence in international travel following recent military events. If they do not discount their prices and consumer confidence in air travel remains low the company expects to sell 1300 holidays at a profit of £60 per holiday. However, if they discount their prices and confidence remains low they expect that they could sell 2500 holidays at a profit of

£35 per holiday. If they do not discount their prices and consumer confidence in air travel recovers they could expect to sell 4200 holidays at a profit of £50. If they do discount their prices and consumer confidence recovers, they could expect to sell 5000 holidays at a profit of £20. Recommend which course of action the company should take with the aid of:

                                                                                                    (Make Pay-off table)

(a) the maximax decision rule

(b) the maximin decision rule

(c) the minimax regret decision rule

(d) the equal likelihood decision rule

why does the t test require the degrees of freedom and the z test does not

Our most accurate information about the current pandemic comes from Italy, where there are 101,739 confirmed cases out of a population of 60 million. This means about 0.17% of the entire population are confirmed cases. Suppose you have 30 extended family members in Italy and each one independently has a 0.17% chance of being a confirmed case. Use binompdf and binomcdf to find the following probabilities:

4a. What is the probability that exactly 0 of your extended family members is a confirmed case?

4b. What is the probability that exactly 10 of your extended family members are confirmed cases?

4c. What is the probability that less than 5 of your extended family members are confirmed cases?

4d. What is the probability that more than 1 of your extended family members are confirmed cases?

4e. What is the probability that between 2 and 4 of your extended family members are confirmed cases?

please show all the steps and in order

Q.5 Let X and Y be continuous rvs with the joint pdf

f(x, y) = 60(x^2)y, for 0 < x, 0 < y, 0 < x + y < 1 and 0 otherwise.

(a) Find E[X + Y ] and E[X − Y ]

(b) Find E[XY ]

(c) Find E[Y |X = x] and E[X|Y = y].

(d) Find Cov[X, Y ]

A) 100 random college students were asked abouttheir breakfast beveragepreferences. 48drink coffee. 28drink orange juice.24drink apple juice. 18 drink orange juice and coffee. 15 drink apple juiceand coffee. 8drink apple and orange juice. 5 drink all three. How many did not drink a beverage?

B) 100 random college students were asked about their breakfast beverage preferences. 48 drink coffee. 28 drink orange juice. 24 drink apple juice. 18 drink orange juice and coffee. 15 drink apple juice and coffee. 8 drink apple and orange juice. 5 drink all three. How many students drink coffee, but not apple juice?

C) 100 random college students were asked about their breakfast beverage preferences. 48 drink coffee. 28 drink orange juice. 24 drink apple juice. 18 drink orange juice and coffee. 15 drink apple juice and coffee. 8 drink apple and orange juice. 5 drink all three. How many students drink coffee, but not orange juice?

2.) Suppose that the number of requests for assistance received by a towing service is a Poisson process with rate a = 6 per hour.

a.) Find the expected value and variance of the number of requests in 30 minutes. Then compute the probability that there is at most one request in 30 minute interval.

b.) What is the probability that more than 20 minutes elapse between two successive requests? Clearly state the random variable of interest using the context of the problem and what probability distribution it follows.

3.) Certain ammeters are produced under the specification that its gauge readings are normally distributed with main 1 amp and variance 0.04 amp^2, respectively.

a.) What is the probability that a gauge reading from the test is more than 1.15 amp?

b.) Find the value of a gauge reading of an ammeter such that 20% of ammeters would have higher readings than that. In other words, find the 80-th percentile of gauge readings.

4. ) Suppose that a quality control engineer believes that the manufacturing process is flawed and wishes to estimate the true mean gauge reading. The engineer samples 130 of these ammeters and measures their gauge readings. From these, the engineer obtains the mean and standard deviation of 1.1 amp and 0.18 amp, respectively. Calculate and interpret a 98% confidence interval for the true mean gauge reading.