Perform t-test on eRPM for Strategy A and B. H0: A = B vs. H1: A != B (Two-sided t-test) What is the p-value?

Choose an organization (Amazon, Sony, etc.) and discuss how they manage large data sets including protocol for transferring data. Select one public data set and examine the technical format and how the data is manipulated globally.

You have 100 coins, and 99 of them are fair (equal probability of heads or tails). One of them is weighted and has a 90% probability of landing on heads. You randomly choose one of the 100 coins. Find the probability that it is a weighted coin, under the following scenarios: (Hint: if your calculator can’t compute 100!, R can, just type factorial(100))

(a) You flip it 10 times and lands on heads 10 times (b) You flip it 10 times and it lands on heads 9 times

(c) You flip it 20 times and it lands on heads 18 times (d) You flip it 100 times and it lands on heads 77 times

Consider the following data set.

a) plot the data (y versus x). Are there any points that appear to be outliers? If there are, circle them and label as such.

b) produce a regression of y against x. Add the regression line to the plot in a). Do you think that the regression line captures the most important features of the data set reasonably well?

c) using calculations at a 5% significance level, can you say that there is a significant linear relationship between the x and y? That is, can you say with 95% confidence that y linearly depends on x? Does this result agree with the conclusion you made in b)?

d) testing at a 5% significance level, can you say that the intercept (β0) is not zero? How does this conclusion agree with the plot in b)?

e) Assume that the first data point is an outlier (e.g. the value was misrecorded). Remove the outlier, and redo the parts b)-d). Plot the data set and both regression lines (before and after the outlier was removed). Comment on the difference. Also comment on the difference between the results of the tests in c) and d), if any.

Perform t-test on eRPM for strategy A and B. H0: A = B vs. H1: A != B (Two-sided t-test) What is the p-value?

#2. The operations manager of a musical instrument distributor feels that demand for a particular type of guitar may be related to the number of YouTube views for a popular music video by the popular rock group Marble Pumpkins during the preceding month. The manager has collected the data shown in the following table: YouTube Views (1000s) Guitar Sales 30 8 40 11 70 12 60 10 80 15 50 13

a. Graph the data to see whether a linear equation might describe the relationship between the views on YouTube and guitar sales.

b. Using the equations presented in this chapter, compute the SST, SSE, and SSR. Find the least squares regression line for the data.

c. Using the regression equation, predict guitar sales if there were 40,000 views last month.

(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.