In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.6% of the general population will live past their 90th birthday. In a graduating class of 735 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday


(b) 30 or more will live beyond their 90th birthday


(c) between 25 and 35 will live beyond their 90th birthday


(d) more than 40 will live beyond their 90th birthday

TABLE 12-3

The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.

Student Co-op Jobs Job Offer

1 1 4

2 2 6

3 1 3

4 0 1

1) Referring to Table 12-3, the least squares estimate of the slope is ________.

2) Referring to Table 12-3, the total sum of squares (SST) is ________.

Write a discussion on the value of knowing how to run and read the results of the ANOVA statistical analysis for today’s marketing agents. Write a discussion on potential shortcomings or weaknesses of the ANOVA analysis and when the marketing agent should and should not use the ANOVA.

Suppose γ is a random variable with Exp(θ) distribution. Conditioning on γ, Y ∼ Poisson(γ). Provide the marginal mean and variance of Y

SAT scores are normally distributed with a mean of 1200 and a variance of 1600. What is the probability that a random sample of 16 scores will yield a mean score less than 1192.5?

During the period 1990–1998 there were 50 Atlantic hurricanes, of which 22 struck the United States. During the period 1999–2006 there were 75 hurricanes, of which 53 struck the United States.

• At α = 0.10, do the data support the hypothesis that the proportion of hurricanes that strike the United States is increasing? Follow and show the 7 steps for hypothesis testing.
• What assumption is required for this test? Show if the assumption is valid.  
• Verify with Minitab, by attaching or including the output.

Using a level of significance of α=0.05, test whether the means of the four types of services are equal. Assume the samples for the four types were independently drawn and that the four populations are normally distributed.

Need Chi-Square Test for Independence to determine if eating healthy and exercising reduces diastolic blood pressure.

The mean and standard deviation of a random sample of n measurements are equal to 33.5 and 3.5, respectively.

a. Find a 90% confidence interval for m if n = 144.

b. Find a 90% confidence interval for m if n = 576.

c. Find the widths of the confidence intervals found in parts a and b.

What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

For each age, calculate the mean number of matings. Take the log of each mean and plot it by AGE. Include your plot.

What assumption can be assessed with this plot? Is there evidence of a quadratic trend on this plot? Explain.

A drink bottler has several devices that pour a specific amount of liquid into each bottle. They test whether the temperature of the liquid has an impact on how much the devices pour. From a sample of the devices, each is tested twice: once with cold liquid, and once with warm. Is there evidence of a difference in the amounts poured at different temperatures? a) What kind of test is this? What are the hypotheses? c) What conditions must be satisfied? d) Assume the sample is representative. Find the p-value and give your conclusion in context.

Warm
21.2
20
19.7
19.7
20.3
20
20.6
17.6
18.4
19.6

Cold
20.6
20.5
19.5
20.1
20.7
19.8
19.9
18.4
19.2
21.3

MGMT 582

Homework: Validation Problem

Pearson’s r

1. Given the following table answer the questions.

1. Calculate Pearson’s Product Movement Correlation Coefficient (r). Show your work.
2. Based on the correlation coefficient which you calculated, in two words how would you describe the relationship between the two variables in the “test”?

2. PHR Score

1. Calculate Pearson’s Product Movement Correlation Coefficient (r). Show your work.
2. Based on the correlation coefficient which you calculated, in two words how would you describe the relationship between the two variables in the “test”?

3. Which of the two “tests” above would you choose? Why?

A random sample of 500 registered voters in Phoenix is ​​asked if they favor the use of
oxygenated fuels throughout the year to reduce pollution. If more than 315 voters
respond positively, we conclude that at least 60% of the voters favor the use of these
fuels.
a) Find the type I error probability if exactly 60% of the voters favor the use of
these fuels.
b) What is the probability of error type II β if 75% of the voters favor this action?

Plot MATINGS by AGE, then add a least squares line. Include your plot.

Is there evidence that modeling matings using a linear regression with age might not be appropriate? Explain. (Hint: Check for a linear trend and for constant variance about the linear fit.)

Both Xand S2 are unbiased for the Poissonλ. Which is better? Use the following steps to answer this question using R.

a) Generate 200000 random numbers from the Poisson(λ= 2) distribution and arrange them in a matrix with 20 rows. Thus you have 10000 samples of size 20.

b) Compute the 10000 sample means and sample variances and store them in objects means and vars, respectively.

c) Compute the average of the 10000 sample means and the average of the 10000 sample variances. Report the two averages. Do they support the claim that they are unbiased for λ= 2?

d) Compute the sample variance of the 10000 sample means and the sample variance of the 10000 sample variances. Report the two variances. Which estimator of λ is preferable?

Please include r code and comments