Classic Golf Inc. manages five courses in the Jacksonville, Florida, area. The director of golf wishes to study the number of rounds of golf played per weekday at the five courses. He gathered the following sample information.

At the 0.05 significance level, is there a difference in the number of rounds played by day of the week?

H₀: Rounds played is the same for each day.
H₁: Rounds played is not the same.

State the decision rule, using the 0.05 significance level.

Compute the value of chi-square.

What is your decision regarding H₀?

An individual possesses 5 umbrellas which he employs in going from his home to the office, and vice versa. If he is at home at the beginning of a day and it is raining, then he will take an umbrella with him to the office provided there is one to be taken. Similarly, if he is at the office and at the end of a day it is raining, he will take one to go home (provided there is one to be taken at the office). If it is not raining, then he never takes an umbrella. Assume that, independent of the past, it rains at the beginning or at the end of a day with probability 0.35.

(a) Define a Markov chain for this system by the construction of the one-step transition matrix (Hint: Define the states of the chain as the number of umbrellas the individual has in the place he is at (home or office). Assume that there is a transition each time he changes places (from home to the office or vice versa)

(b) Find the steady state probabilities, by the formulation of the steady state equations.

(c) What fraction of time does the man get wet? Justify your answer

A statistics instructor wonders whether significant differences exist in her students’ final exam scores in her three different sections. She randomly selects the scores from 10 students in each section. A portion of the data is shown in the accompanying table. Assume exam scores are normally distributed.

Construct an ANOVA table. (Round "Sum Sq" and "Mean Sq" to 1 decimal place, "F value" to 3, and "p-value" to 3 decimal places. Before fitting your model, type options(scipen=10) and options(digits=10) into your R console.)

(15.48 S-AQ) The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean µ = 298 and standard deviation s = 34.

1. Choose one 12th-grader at random. What is the probability (± ± 0.1) that his or her score is higher than 298? Higher than 332 (± ± 0.001)?

2. Now choose an SRS of 16 twelfth-graders and calculate their mean score x⎯⎯⎯ x ¯ . If you did this many times, what would be the mean of all the x⎯⎯⎯ x ¯ -values?

3. What would be the standard deviation (± ± 0.1) of all the x⎯⎯⎯ x ¯ -values?

4. What is the probability that the mean score for your SRS is higher than 298? (± ± 0.1) Higher than 332? (± ± 0.0001)

A recent survey showed that among 700 randomly selected subjects who completed 4 years of college, 151 smoke and 549 do not smoke. Determine a 95% confidence interval for the true proportion of the given population that smokes. 95% CI: to

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.00 ml/kg for the distribution of blood plasma.

(a) Find a 95% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Use 2 decimal places.)

(d) Find the sample size necessary for a 95% confidence level with maximal/marginal error of estimate E = 2.80 for the mean plasma volume in male firefighters.

You wish to test the claim that mu equals880 at a level of significance of alpha equals0.01 and are given sample statistics n equals 35 and x overbar equals 850. Assume the population standard deviation is 82. Compute the value of the standardized test statistic. Round your answer to two decimal places. You wish to test the claim that mu equals880 at a level of significance of alpha equals0.01 and are given sample statistics n equals 35 and x overbar equals 850. Assume the population standard deviation is 82. Compute the value of the standardized test statistic. Round your answer to two decimal places.

A company has 2 types of machines that produce the same product, one recently new and another older. Based on past data, the older machine produces 12% defective products while the newer machine produces 8% defective products. Due to capacity needs, the company must use both machines to meet demand. In addition, the newer machine produces 3 times as many products as the older machine.  

1. Setup a probability table depicting the machine type and defective outcome
2. Given a randomly selected product was tested and found to be defective, what is the probability it was produced by the new machine?
3. What is the probability that any selected product is defective (regardless of machine type)?
4. What is the probability that any selected product is non-defective and produced by the older machine?     

Math & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a two-tailed test.

This is a right-tailed test.    

This is a left-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t = ?

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value = ?

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.    

We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

The sampled population is normally distributed, with the given information. (Give your answers correct to two decimal places.)

n = 11, x = 29.6, and σ = 6.4

(a) Find the 0.99 confidence interval for μ.
to  

QUESTION 12

1. A teacher would like to estimate the mean grade for her class of 50 students on the most recent exam. After the first 10 tests are graded (in random order), her sample results are as follows:

   45 60 74 75 79 80 85 86 90 96

   Which of the numbers below represent the point estimate?

   	A.	15.4
   	B.	77.0
   	C.	84.0
   	D.	79.5

4. Let N be a Poisson(λ) random variable. We observe N, say it equals n, we then throw a p-biased coin n times and let X be the number of heads we get. Show that X is a Poisson(pλ) random variable. (You can use the following identity: ∑ ∞ k=0 (y^k)/ k! = e^y .)

A reporter estimates that professional golfers have an average height of 70.1 inches, with a variance of 7.17. To test this estimate, a researcher chooses a random sample of 22 professional golfers and finds that their mean height is 70.2 inches, with a variance of 10.40. Do these data provide enough evidence, at the 0.1 level of significance, to reject the claim that the true variance, σ2, of professional golfers' heights is equal to 7.17? Assume that the heights of professional golfers are approximately normally distributed.Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

A random sample of 36 observations is drawn from a population with a mean equal to 51 and a standard deviation equal to 15.

1. What is the mean and the standard deviation of the sampling distribution of x̄?

1. Calculate the z-score corresponding to a value of x̄ = 45.5.
   
   
2. Calculate the z-score corresponding to a value of x̄ = 46.5.
   
   
3. Find P(x̄ ≥ 45.5) (to 4 decimals)
   
   
4. Find P(x̄ < 46.5) (to 4 decimals)
   
   
5. Find P(45.5 ≤ x̄ ≤ 46.5) (to 4 decimals)
   
   
6. There is a 60% chance that the value of x̄ is above  (to 4 decimals).

Assume a 2015 Gallup Poll asked a national random sample of 491 adult women to state their current weight. Assume the mean weight in the sample was ?¯=161.

We will treat these data as an SRS from a normally distributed population with standard deviation ?=36 pounds.

Give a 99% confidence interval for the mean weight of adult women based on these data. Enter the upper and lower values of your confidence interval into the spaces provided rounded to two decimal places.

lower value = pounds

upper value = pounds

Do you trust the interval you computed as a 99% confidence interval for the mean weight of all U.S. adult women? Select an answer choice that correctly explains why or why not.

This interval can be trusted since a 99% confidence interval can be expected to be relatively accurate.

This interval would probably be more trustworthy if the poll contacted women with a wider range of different weights.

This interval can be trusted and seen to be around 99% accurate.

There is probably little reason to trust this interval; it is possible that many of the women either wouldn’t know their current weight or would lie about it.