(1) The table below is a probability distribution of potential quantity of sales of Gourmet sausages during a game. John Bull has to pay a concession fee of $200 to receive a permit to sell sausages at the stadium. Gourmet sausages can be bought at wholesale for $2.00 and sold in the stadium for $3.50 each. Unsold sausages cannot be returned. Given the probability distribution:

1. How many sausages should John Bull expect to sell?
2. How many sausages should John Bull purchase? Gourmet sausages can only be purchased in batches of 50 units as indicated in the probability distribution.

1. The president of a national real estate company wanted to know why certain branches of the company outperformed others. He felt that the key factors in determining total annual sales ($ in millions) were the advertising budget (in $1000s) X₁ and the number of sales agents X₂. To analyze the situation, he took a sample of 25 offices and ran the following regression. The computer output is below.

            PREDICTOR            COEF             STDEV                       P-VALUE

            Constant                    -19.47             15.84                          0.2422

            X₁                                0.1584            .0561                          0.0154

            X₂                                0.9625            .7781                          0.2386

            S_e = 7.362                             R squared = .524                             Sig F = 0.0116

(a)What are the anticipated signs for each of the independent variables in the model?

(b) Interpret the slope coefficient associated with the number of real estate agents.

(c) Test to determine if a positive relationship exists between the advertising spending and annual sales. Use alpha = .05.

(d) Can we conclude that this model explains a significant portion of the variation in annual sales? Use alpha =.01.

graduate student wants to estimate the number of research participants he will see in the fall semester. Using his data from the previous nine semesters, he tabulates a mean of 140 students per semester, although departmental records reflect a seasonal variation (i.e., population standard deviation) of 45 students. Calculate the 99% confidence interval.

Suppose a consumer advocacy group would like to conduct a survey to find the proportion of consumers who bought the newest generation of an MP3 player were happy with their purchase. Their survey asked consumers if they were happy or unhappy with their purchase. The responses indicated 28 out of 70 customers reported being unhappy with their purchase. Compute a 90% confidence interval for the population proportion of consumers who are happy with their purchase.

(.2492, .5508)

(.4852, .7148)

(.5037, .6963)

(.3037, .4963)

The University of Arkansas recently approved out of state tuition discounts for high school students from any state. The students must qualify by meeting certain standards in terms of GPA and standardized test scores. The goal of this new policy is to increase the geographic diversity of students from states beyond Arkansas and its border states. Historically, 90% of all new students came from Arkansas or a bordering state. Ginger, a student at the U of A, sampled 180 new students the following year and found that 157 of the new students came from Arkansas or a bordering state. Does Ginger’s study provide enough evidence to indicate that this new policy is effective with a level of significance 10%? What would be the correct decision?

1. An instructor would like to examine the effect of using handouts during lecture on student’s grades. Usually no handouts are used and the mean final grade in the class is μ = 80. This semester, the instructor uses handouts during lecture and the mean final grade in the class of n = 41 students is M = 82.5 with a standard deviation of s = 6.

a. Is there sufficient evidence to conclude that handouts significantly (α = .01) change overall grades? If so, compute the effect size (r²) and explain what it tells you about the differences in grades due to handouts.

1.

2.

3.

4.

b. Is there sufficient evidence to conclude that handouts significantly (α = .01) improve overall grades? (Hint: Step 3 will be the same as part a.)? If so, compute the effect size (r²) and explain what it tells you about the differences in grades due to handouts.

1.

2.

3.

4.

-The weight of an organ in adult males has a​ bell-shaped distribution with a mean of

300 grams and a standard deviation of 40 grams. Use the empirical rule to determine the following.

a. About 95% of organs will be between what​ weights?

b. What percentage of organs weighs between 260 grams and 340 ​grams?

​(c) What percentage of organs weighs less than 260 grams or more than 340 ​grams?

​(d) What percentage of organs weighs between 220 grams and 340 ​grams?

-Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 12.

Use the empirical rule to determine the following.​

(a) What percentage of people has an IQ score between 88 and 112​?

​(b) What percentage of people has an IQ score less than 88 or greater than 112​?

​(c) What percentage of people has an IQ score greater than 112

-Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 800 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 475 grams. If a 33​-week gestation period baby weighs 3075 grams and a 41​-week gestation period baby weighs 3275 ​grams, find the corresponding​ z-scores. Which baby weighs more relative to the gestation​ period?

-In a certain​ city, the average​ 20- to​ 29-year old man is 69.8 inches​ tall, with a standard deviation of 3.0 ​inches, while the average​ 20- to​ 29-year old woman is 64.5 inches​ tall, with a standard deviation of 3.9 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

-A manufacturer of bolts has a​ quality-control policy that requires it to destroy any bolts that are more than 4 standard deviations from the mean. The​ quality-control engineer knows that the bolts coming off the assembly line have mean length of 12 cm with a standard deviation of 0.05 cm. For what lengths will a bolt be​ destroyed?

Real Fruit Juice: A 32 ounce can of a popular fruit drink claims to contain 20% real fruit juice. Since this is a 32 ounce can, they are actually claiming that the can contains 6.4 ounces of real fruit juice. The consumer protection agency samples 44 such cans of this fruit drink. Of these, the mean volume of fruit juice is 6.33 with standard deviation of 0.19. Test the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces. Test this claim at the 0.05 significance level.

(a) What type of test is this?

This is a left-tailed test.

This is a right-tailed test.

This is a two-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.

t x =

(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.

There is enough data to justify rejection of the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

There is not enough data to justify rejection of the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

We have proven that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

We have proven that the mean amount of real fruit juice in all 32 ounce cans is not 6.4 ounces.

A poll surveyed people in six countries to assess attitudes toward a variety of alternate forms of energy. Suppose the data in the following table are a portion of the poll's findings concerning whether people favor or oppose the building of new nuclear power plants.

(a)

How large was the sample in this poll?

(b)

Conduct a hypothesis test to determine whether people's attitude toward building new nuclear power plants is independent of country.

State the null and alternative hypotheses.

H₀: The attitude toward building new nuclear power plants is mutually exclusive of the country.
H_a: The attitude toward building new nuclear power plants is not mutually exclusive of the country.H₀: The attitude toward building new nuclear power plants is not mutually exclusive of the country.
H_a: The attitude toward building new nuclear power plants is mutually exclusive of the country.    H₀: The attitude toward building new nuclear power plants is not independent of the country.
H_a: The attitude toward building new nuclear power plants is independent of the country.H₀: The attitude toward building new nuclear power plants is independent of the country.
H_a: The attitude toward building new nuclear power plants is not independent of the country.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We conclude that the attitude toward building new nuclear power plants is not independent of the country.Do not reject H₀. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country.    Reject H₀. We conclude that the attitude toward building new nuclear power plants is not independent of the country.Reject H₀. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country.

(c)

Using the percentage of respondents who "strongly favor" and "favor more than oppose," which country has the most favorable attitude toward building new nuclear power plants?

Great BritainFrance    ItalySpainGermanyUnited States

Which country has the least favorable attitude?

Great BritainFrance    ItalySpainGermanyUnited States

A farmer randomly samples 600 eggs and finds that 28 are bad. Find a 95% confidence interval for the actual proportion of bad eggs.

1.A random sample of size 120 is drawn from a large population with mean 38.75 obtain the sd of the distribution of all possible sample mean ( let the sample sd be s= 5.28 ) what is the sampling distribution of the mean?

2. In a random sample of size 506, the average cholesterol level of group of adults is 96.997 if the standard deviation of the colesterol level in the city adults population is 1.74 find the 72% confidence for u

Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of cars each of the cars types. The data below displays the frontal crash test performance percentages.

Patrick wants to purchase a new car, but he is concerned about safety ratings. Using the data from the chart above, what would you recommend to Patrick if he is debating between compact, midsize, and full-size cars? FYI: High scores on crash performance tests are GOOD. (Higher scores means they passed the test a higher percent of the time.)

1. Evaluate all three types of car in your response using One-Way ANOVA and follow-up t-tests. 2. Explain why you gave him this suggestion.

The survival rate of a cancer using an existing medication is known to be 30%. A pharmaceutical company claims that the survival rate of a new drug is higher. The new drug is given to 15 patients to test for this claim. Let X be the number of cures out of the 15 patients. Suppose the rejection region is {8 }.≥X a. State the testing hypotheses. b. Determine the type of error that can occur when the true survival rate is 25%. Find the error probability. c. Determine the type of error that can occur when the true survival rate is 30%. Find the error probability. d. Determine the type of error that can occur when the true survival rate is 40%. Find the error probability. e. What is the level of significance?

In 2009, the Southeastern Conference (SEC) commissioner set a goal to have greater than 65% of athletes that are entering freshmen graduate in 6 years. In 2015, a sample of 100 entering freshmen from 2009 was taken and it was found that 70 had graduated in 6 years. Does this data provide evidence that the commissioner’s graduation goal was met (α = .10)?

The value of the test statistic is ________ and the critical value is _________.