A total of 23 Gossett High School students were admitted to State University. Of those students, 7 were offered athletic scholarships. The school’s guidance counselor looked at each group’s summary statistics of their composite ACT scores, wondering if there was a difference between the groups (those who were not offered scholarships and those who were). The statistics for the 16 students who were not offered scholarships are x̅ = 24.7, s = 2.8 and for the 7 who were, x̅ = 26.5, s = 2.6. Assume that both distributions are approximately normal. Test the counselor’s claim using a 90% Level of Confidence.

We use statcrunch and the p method for homework.

How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

67 107 130 129 60 64

Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.) x = lb s = lb

(b) Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.) lower limit lb upper limit lb

Probability and Decision Analysis

A smartphone supplier in Sydney is considering three alternative investment options: a large store, a small store, or an outlet in the shopping mall.  

Profits from selling smartphones will be affected by the customer demand for smartphones in Sydney. The following payoff table shows the profit that could result from each investment, in dollars ($).  

1. What choice should be made by the optimistic decision maker?

2. What choice should be made by the pessimistic decision maker?

3. Compute the regrettable from the data.

4. What decision should be made under minimax regret approach?

5. What choice should be made under the expected value approach?

With excel

1: Explain the term ‘autoregression’ in a time series regression context.

2. Explain the term ‘autocorrelation’ and the problems it creates when using OLS regression in time series data.

1. The table shows the number of computers per household in the United States.

1. Construct a probability distribution.
2. Graph the probability distribution using a histogram and describe its shape.
3. Find the mean, variance, and standard deviation of the probability distribution and interpret the results.
4. Find the probability of randomly selecting a household that has at least four computers.

1. A sample of 25 seniors from a large metropolitan area school district had a mean Math SAT score of 450. Suppose we know that the standard deviation of the population of Math SAT scores for seniors in the district is 100. A 90% confidence interval for the population mean SAT score for the population of seniors is used. Which of the following would produce a confidence interval with a smaller margin of error?                                                                                                    (2)

1. Using a sample of 100 seniors
2. Using a confidence level of 95%
3. Using an alpha (α) of 0.01
4. Using a sample of only 10 seniors

2. In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. What is the sampling distribution of their sample mean IQ? Must show work (explain) to justify choice.                                           (4)

1. exactly normal, mean 112, standard deviation 20
2. approximately normal, mean 112, standard deviation of 0.1
3. approximately normal, mean 112, standard deviation 1.414
4. approximately normal, mean 112, standard deviation 20

3. A final exam in Math 160 has a mean of 73 with a standard deviation of 7.8. If 34 students are randomly selected, find the probability that the mean of their test scores is more than 76.   (6)

4. Given that a piece of data is from a distribution with a mean of 0 and a standard deviation of 1, find the amount of area under the curve between z = – 1.83 and z = 0.                                 (3)

5. A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases to have a distribution that appears to be bell-shaped with a mean of $9004 and a standard deviation of $5629. Construct the 99% confidence interval for the mean of all such costs.                                                                                         

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 4 percentage points with 99​% confidence if

he uses a previous estimate of 38%?

​(b) He does not use any prior​ estimates?

# Please I need the answer by Excel with showing steps.

The average American man consumes 9.5 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N( , )

b. Find the probability that this American man consumes between 8.6 and 9.5 grams of sodium per day.

c. The middle 20% of American men consume between what two weights of sodium? Low: High:

1. Presume that the following data were collected from respondents to a poll asking for their rating of the current state of the economy, ranging from 1 to 100 (1= worst, 100 = best).

1). State your hypotheses for the effect of party affiliation:

      H₀:

      H₁:

2). Test your hypothesis using a one-way ANOVA. Show all your work andenter your information in the appropriate boxes:

MS_B:                  

MS_W:                  

F:                       

df:               ,       

F_crit:                   

3). What is your conclusion regarding H₀?    (Circle one):    RETAIN     REJECT

4). What is your conclusion regarding the research hypothesis?

2. In an ANOVA, what do “within-groups variability” and “between-groups variability” mean?

3. Describe how the F-distribution is different than the t-distribution. There is at least one feature that they share in common, however (and the z-distribution does not have this feature). What is it?

QUESTION 4 ( 8 marks)

A telemarketer is able make a sale on 28% of the phone calls he makes. Assume that he makes 11 calls in an hour. Answer the following questions, assuming a binomial probability distribution:

Required:

1. What is the probability that he will make exactly four sales in the course of an hour? ( 3 marks)

2. What is the probability that he will make at least three sales in the course of an hour? Hint: Use the approach that requires the least calculation work! ( 5 marks)

QUESTION 5 ( 8 marks)

Suppose 1.5% of the antennas on new Nokia cell phones are defective. For a random sample of 240 antennas, answer the following questions (assume a Poisson probability distribution):

Required:

1. Calculate the mean and standard deviation for the probability distribution of the number of defective antennas in the random sample. and What is the probability that exactly five of the antennas will be defective? ( 4 marks)
2. What is the probability that less than three antennas will be defective? ( 4 marks)

QUESTION 3

A recent study shows that on average 20% of employees in the work population prefer their vacation time during March break. Vincent Company employs 56 people. Use the normal approximation to the binomial distribution to answer the questions below:

Required:

1. Determine the expected value, and the standard deviation of that value, of the number of Vincent Company employees who would prefer their vacation time during March break. ( 3 marks)

2. What is the probability that more than ten Vincent Company employees will prefer their vacation during March break? Sketch a normal curve and shade the desired area of your diagram. ( 4 marks)

3. What is the probability that exactly ten Vincent Company employees will prefer their vacation during March break? Sketch a normal curve and shade the desired area of your diagram.   ( 4 marks)
4. What is the probability that more than five, but less than nine, Vincent Company employees will prefer their vacation during March break? Sketch a normal curve and shade the desired area of your diagram.   ( 4 marks)

A dog food manufacturer is using a new process to make his dog food.  He believes the new process affects the taste of the food.  To test the new process, the company recruited 9 dogs. The dogs were given the original food and the time required to eat a standard portion of the food was measured. Two days later the same dogs were fed the same quantity of the new formula and the time was measured again. Eating faster is assumed to mean the taste was better.  Eating slower means the taste was worse The times are below. Test the hypothesis that the new process affects the taste of the dog food using an alpha level of .05.

MAKE SURE TO ANSWER ALL OF THE QUESTIONS. SHOW YOUR WORK WHERE POSSIBLE.

a) What is the appropriate test?

b) State the null hypothesis (in words and with means).

c) State the alternative hypothesis (in words and with means).

d) Find the critical value(s) (explain how you found it).

e) Calculate the obtained statistic (show all of your work).

f) Report the results in proper format. Make a decision.

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century.

A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years. Suppose that it is somehow known that the population standard deviation is 1.5 years.

Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal. Use a 1% level of significance.

a.) What is α? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

αα =

H0H0: μμ =

H1H1: μμ Select an answer > not = <  

The test is a Select an answer left-tailed right-tailed two-tailed  test

b.) Identify the Sampling Distribution you will use. What is the value of the test statistic?

The best sampling distribution to use is the Select an answer Student's t Normal  distribution.

The test statistic (z or t value) is =

c.) Find or estimate the P-value for the test.

The p-value is =

d.) Conclude the test.

Based on this we will Select an answer Reject Fail to reject  the null hypothesis.

How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 54readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 22°C.

(a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)

(b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will go up or down? Explain.

It will go up because hot air will make the balloon rise.It will go up because hot air will make the balloon fall.    It will go down because hot air will make the balloon fall.It will go down because hot air will make the balloon rise.