Maximize p = 14x + 10y + 12z subject to

P=

(x,y,z)=

A sample has a mean of M = 60 and a t statistic of t = 4.5. For a one-tailed hypothesis test with α = .01, what is the correct statistical decision for this sample? Why?

Why?

A political analyst was curious if younger adults were becoming more conservative. He decided to see if the mean age of registered Republicans was lower than that of registered Democrats. He selected an SRS of 128 registered Republicans from a list of registered Republicans and determined the mean age to be /X1 = = 39 years, with a standard deviation s₁ = 8 years. He also selected an independent SRS of 200 registered Democrats from a list of registered Democrats and determined the mean age to be /2 = 40 years, with a standard deviation s₂ = 10 years. Let μ1 and  μ2 represent the mean ages of the populations of all registered Republicans and Democrats, respectively. Suppose that the distributions of age in the populations of registered Republicans and of registered Democrats have the same standard deviation. Assume the pooled two-sample t procedures are safe to use.

Suppose the researcher had wished to test the hypotheses:

H₀: μ1= μ2, H_{a, :} μ1 < μμ2 .

The P-value for the pooled two-sample t test is:

a. larger than .10

b. between 0.05 and .10

c. between 0.01 and 0.05

d. below 0.01

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1. Construct two QQ‐plots, one displaying the durations of the games Sven won, and another displaying the durations of the games Jens won. (Note: When making the QQ‐ plots, treat them as two separate datasets.)

2. Using the QQ‐Plots, is it plausible to conclude that the distribution of duration for the games Sven won follows a Normal Distribution? Analogously, is it plausible to conclude that the distribution of duration for the games Sven won follows a Normal Distribution?

The following data are given for a two-factor ANOVA with two treatments and three blocks.

Using the 0.05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ.

1. State the null and alternate hypotheses for treatments.

2. State the decision rule for treatments. (Round your answer to 1 decimal place.)

3. State the null and alternate hypotheses for blocks. (Round your answer to 1 decimal place.)

Also, state the decision rule for blocks.

1. d & e. Compute SST, SSB, SS total, and SSE and complete an ANOVA table. (Round your SS, MS values to 3 decimal places and F value to 2 decimal places.)

6. Give your decision regarding the two sets of hypotheses.

According to the National Health Statistics Reports, the standard deviation of the weights of all one-year-old baby boys born in the U.S. is 5.3 pounds. A random sample of 360 one-year-old baby boys born in the U.S. had a mean weight of 25.5 pounds.

a) Construct a 90% confidence interval for the mean weight of all one-year-old baby boys in the U.S. Write a sentence that interprets this interval.

b) Should this confidence interval be used to estimate the mean weights of all one-year-old babies in the U.S.? Explain.

A psychic was tested for ESP. The psychic was presented with 400 cards face down and was asked to determine if the card was one of four symbols: a cross, a star, a circle, or a square. The psychic was correct in 120 of the cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.

A. Using the results above, construct a 99% confidence interval for p.

B. How large a sample n would you need to estimate p with a margin of error of 0.01 with 95% confidence? (Use the guess 0.25 as the value of p)

1. A social science researcher collected data from a random sample of 400 students at a large university and found that, on average, they belonged to 2.6 campus organizations. The standard deviation σ for the population is 1.8.

1. Using these data, construct a 95% confidence interval for µ, the mean number of campus organizations belonged to by the population of students at this university.

2. Write a sentence to interpret your confidence interval, making sure to provide all the important information.

In a survey of 517 music teachers, 403 said that the video games Guitar Hero and Rock Band have a positive effect on music education. Construct a 98% confidence interval for the proportion of music teachers who believe that these video games have a positive effect. Write a sentence that interprets this interval.

High School A and High School B both claim that they are superior. Last year School A had 354 students take an AP exam and 231 passed. School B had 684 students take the same exam and 512 passed.

Is this within natural variation? Or is this evidence that School B has a statistically significant higher passing rate? Report the p-value.

An Izod Impact Test was performed on 20 specimens of PVC pipe. The sample mean is ? = 1.25, and the sample ??? ??????? ? standard deviation is ? = 0.25. You need to test if the true mean Izod Impact Strength is less than 1.5.

a.Write down the Null and Alternative Hypotheses to be tested

b.What is the appropriate type of statistical test? Explain.

c.Construct a 95% ?????????? ???????? and test the Hypotheses. Clearly interpret the test result.

d.Test the Hypotheses using the Test Statistic method. Do you get the same answer as part (c)?

c. What is the ? ????? for the test? Do you get the same answer as parts (c) and (d)?

A multiple

-choice test question has four possible responses. The question is designed to be very

difficult, with none of the four responses being obviously wrong, yet with only one correct

answer. It first occurs on an exam taken by 400 stude

nts. The designers test whether more

people answer the question correctly than would be expected just due to chance (i.e., if

everyone randomly guessed the correct answer).

a)

Set up the hypotheses for the test.

b)

Of the 400 students, 125 correctly answer

the question. Find the P

-value, and interpret.

c)

Make a decision about H0, using α = .05. Based on this decision, what can you conclude

about the parameter?

"To Breakfast or Not to Breakfast?" by Richard Ayore

In the American society, birthdays are one of those days that everyone looks forward to. People of different ages and peer groups gather to mark the

18^th, 20^th,   ,

birthdays. During this time, one looks back to see what he or she has achieved for the past year and also focuses ahead for more to come.

If, by any chance, I am invited to one of these parties, my experience is always different. Instead of dancing around with my friends while the music is booming, I get carried away by memories of my family back home in Kenya. I remember the good times I had with my brothers and sister while we did our daily routine.

Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he came to weed. He said, "This is why I always work more hours than you guys!"

And so, to prove him wrong or right, we decided to give it a try. One day we went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. On the next day, we all ate breakfast before going to work. We recorded how long we worked again before getting tired and stopping. Of interest was our mean increase in work time. Though not sure, my brother insisted that it was more than two hours. Using the data in the table below, solve our problem. (Use

α = 0.05)

• State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

• Part (e)

  What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

• Part (f)

  What is the p-value?

Following are the number of grams of carbohydrates in a sample of 12-ounce espresso beverages offered at Starbucks.

6, 7, 19 , 20, 22, 25, 27, 38 , 48, 59

Compute the IQR. Write only a number as your answer.

In studying his campaign plans, Mr. Singleton wishes to estimate the difference between men's and women's views regarding his appeal as a candidate. He asks his campaign manager to take two random independent samples and find the 90% confidence interval for the difference. A random sample of 588 male voters and 545 female voters was taken. 273 men and 322 women favored Mr. Singleton as a candidate. Find this confidence interval. Step 3 of 4 : Find the value of the standard error. Round your answer to three decimal places