(1 point) Fireworks. Last summer, Survey USA published results of a survey stating that 229 of 416 randomly sampled Kansas residents planned to set off fireworks on July 4th. Round all results to 4 decimal places.

1. Calculate the point estimate for the proportion of Kansas residents that planned to set off fireworks on July 4th

2. Calculate the standard error for the point estimate you calculated in part 1.

3. Calculate the margin of error for a 99 % confidence interval for the proportion of Kansas residents that planned to set off fireworks on July 4th.

4. What are the lower and upper limits for the 99 % confidence interval.

( ,  )

5. Use the information from Survey USA poll to determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than 4.2%. For consistency, use the reported sample proportion for the planning value of p* (rounded to 4 decimal places) and round your Z-value to 3 decimal places. Your answer should be an integer.

The data below are the densities of clover flowers in a lawn (flowers/m2) for 20 quadrat samples. For this data set create a frequency table and histogram, and determine the sample size, mean, median, mode, range, standard deviation, variance, and standard error, and the 95% confidence interval for the population mean. Describe the data using all of the following terms that apply: population, census, sample, quantitative data, qualitative data, discrete data, continuous data, symmetric, skewed, bimodal, and/or multimodal.

5, 0, 23, 10, 1,

6, 19, 0, 4, 8,

0, 18, 22, 23, 0,

21, 7, 24, 6, 23

1. You work for the Colorado Chapter of the Mutual UFO Network (MUFON) that is responsible for compiling all UFO sightings in the US. You are interested in whether there is a difference between rural and urban people in the mean number of UFOs they have ever seen. You randomly sample 200 urban and 150 rural Coloradoans and ask how many UFOs they’ve seen. Of the urbanites, the mean number of UFOs is 1.3 UFOs with a standard deviation of .4. Of the rural folks, the mean number of UFOs is 1.5 UFOs with a standard deviation of .6.

Do a two-sample hypothesis test (alpha=.05) to determine whether you can claim that there is a difference urban and rural Coloradoans in the mean number of UFOs ever seen. You must show all steps and all calculations.

2. You are interested in studying the relationship between believing in aliens and believing in God. You randomly sample 400 Coloradoans and ask them whether they believe in aliens and whether they believe in God. Of the 290 people who believe in God, 83 said they believed in aliens. Of the 110 people who do not believe in God, 27 said they believe in aliens.

Do a two-sample hypothesis test (alpha=.05) to determine whether there’s a difference between those who believe in God and those who don’t in the percent who believe in aliens. Show all steps of the hypothesis test and all calculations.

Independent trials, each of which is a success with probability p, are successively performed. Let X denote the first trial resulting in a success. That is, X will equal k if the first k −1 trials are all failures and the kth a success. X is called a Geometric random variable (google it). Determine the moment generating function of X.

Consider a random sequence x1,…,x7 of 7 numbers each chosen from the set {1,2,3,…,10} with replacement. What is the probability that max{x1,…,x7} occurs exactly once in x1,…,x7?

1 - A 95% confidence interval for a population proportion was constructed using a sample proportion from a random sample. Which of the following statements are correct? Select all that apply.

A) We don't know if the 95% confidence interval actually does or doesn't contain the population proportion.

B) The population proportion must lie in the 95% confidence interval.

C) There is a 95% chance that the 95% confidence interval actually contains the population proportion.

D) The sample proportion must lie in the 95% confidence interval.

E) If we were to use a 90% confidence level, the confidence interval from the same data would produce an interval wider than the 95% confidence interval.

2 - Public Policy Polling recently conducted a survey asking adults across the U.S. about music preferences. When asked, 83 of the 574 participants admitted that they have illegally downloaded music.
* Create a 99% confidence interval for the true proportion of American adults who have illegally downloaded music. (Round your answers to two decimal places.)

( _____ , _____ )

You may need to use the appropriate Appendix Table to answer this question.

* Which of the following statement is true about the confidence interval in part (a)?

A) This confidence interval contains the true population proportion.

B) The sample proportion may or may not be in this confidence interval.

C) There is a 99% chance that the true population proportion lies in this confidence interval.

D) This confidence interval may not contain the true population proportion.

On average, a student takes 100 words/minute midway through an advanced court reporting course at the American Institute of Court Reporting. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 20 words/minute, find the probability that a student randomly selected from the course can take dictation at the following speeds. (Round your answers to four decimal places.)

(a) more than 140 words/minute

(b) between 40 and 140 words/minute

(c) less than 40 words/minute

Let N1 , N2 , N3 follow a trinomial distribution with parameters n, assume that n follows a Poisson distribution with parameter λ > 0. Also assume that, conditionally on N, the random variables N1, N2, N3 follow a trinomial distribution with N trials and category probabilities p1, p2, p3 with p1 + p2 + p3 = 1. Compute the covariance and correlation of (N1,N2)

True or False

(a) For any distribution, the sample data, Y1, . . . Yn, is always a sufficient statistic.

(b) Biased estimators are always preferred to unbiased estimators.

(c) Maximum likelihood estimators are always unbiased.

please make sure to do the p values. this is what I need to fill in:

A sociologist wishes to see if it is true that for a certain group of professional women, the average age at which they have their first child is 28.6 years. A random sample of 36 women is selected, and their ages at the birth of their first child are recorded. At α = 0.05, does the evidence refute the sociologist’s assertion?

Ages at birth 32   28   26   33   35   34   29   24   22   25   26   28   28   34   33   32   30   29   30   27   33   34   28   25   24   33   25   37   35   33 34   36   38   27   29   26

Random sample 2 numbers from {1,3,5,7} with Replacement.

1. Write down every sample means and sample variances about all possible samples.
2. Write down Mean of sample means and Variance of sample means.

All answers should be presented with process.

The editor of a text publishing company in USA is trying to decide whether to publish a proposed business statistics book. Information on previous textbooks published indicated that 10% are huge success, 20% are moderate success, 40% break even and 30% are losers. However, before publishing decision is made, the text books will be reviewed. In the past, 99% of the huge success received favorable reviews, 70% of the moderate success received favorable reviews, 40% of the break-even books received favorable reviews, and 20% of the losers received favorable reviews

a. If the proposed textbook receives a favorable review, show should the editor revise the probabilities of the various outcomes to take this information into account? Explain.

b. What proportion of textbooks receives favorable reviews?

Please provide excel formulas and your explanation on the Question a.

Thank you in advance.

A recent survey of 200 companies showed that 8 had a female as the head of the company. A year ago, a survey of 200 companies showed that 6 had a female as the head of the company. At α = 0.05, can it be concluded that the proportion has changed? Find the 95% confidence interval of the difference of the two proportions.