According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)

Compute the probability that exactly two of the six M&M’s are red. ________

Compute the probability that two or three of the six M&M’s are red. _______

Compute the probability that at most two of the six M&M’s are red. _______

Compute the probability that at least two of the six M&M’s are red. _______

If you repeatedly select random samples of six peanut M&M’s, on average how many do you expect to be red? (Round your answer to two decimal places.) ____red M&M’s

With what standard deviation? ________(Round your answer to two decimal places.) red M&M’s

1. Consider simple regression model (one independent variable)

a) How do you find a confidence interval for the coefficient of X?

b) How do you conduct a test if the coefficient of X is 10 or not?

c) How do you find a CI for the mean of the dependent variable if x=2?

The following is the regression output for a study on serious crime rates in cities in the United States. The data was collected in the 1970s. AREA is the size of the city, DOCS is the number of Doctors, % > 65 is the proportion of residents greater than 65 years of age and HOSPITAL BEDS is the number of hospital beds per population. Answer the following questions given the supplied regression output. These variables are regressed on the serious crime rates in an attempt to explain variance in crime rates in different cities. (3 points per question)

1. How accurate is regression model? What amount of the variance in Serious Crimes is explained
2. How strong is the linear relationship between the predictors and Serious Crimes?
3. How close to the regression line is the majority of observations?
4. Does the model fit the data better than not using these predictor variables? Is the F-test significant? What hypothesis can we draw from it?
5. Use the output to form the regression equation.
6. Are all the predictors significant? Is zero contained in the confidence intervals? Why is that interesting?
7. Of the significant variables, does the corresponding slopes make intuitive sense?   Are the effects of the predictors reasonable?
8. How much variance in serious crime is unaccounted for? What additional data might explain some of this remaining variance?

The following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study).

Do not forget to convert this table from parallel format (i.e., groups in each column) to serial format for analysis in SPSS.

Use SPSS (or another statistical software package) to conduct a one-factor ANOVA to determine if the group means are equal using α=0.05. Though not specifically assessed here, you are encouraged to also test the assumptions, plot the group means, and interpret the results.

Group means (report to 2 decimal places):
Group 1: Internship:
Group 2: Co-op:
Group 3: Work Study:


ANOVA summary statistics:

F-ratio =
(report accurate to 3 decimal places)
p=
(report accurate to 4 decimal places)

Conclusion:

a.There is not sufficient data to conclude the starting wages are different for the different groups.

b. The sample data suggest the average starting hourly wages are not the same.

A local grocery store wants to predict the monthly sales in dollars. The manager believes that the amount of newspaper advertising significantly affects the store sales. The manager randomly selects 10 months of data consisting of monthly grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). See the following data:

If the advertising expenditures increase by one thousand of dollars, estimate the average increase in sales with 95% confidence.

The next month, the grocery store wants to invest 3230 dollars in advertising. Predict the total sales for that specific month with 95% confidence.

At the 5% level of significance, conduct the F test to test the overall significance of the model. Is the current model a significant predictor of of the monthly grocery store sales?

Use this scenario to answer questions below.

The Collins Research Crew (CRC) is interested in examining the number of vape/smoking stores (i.e. stores that sell vaping and cigarette/cigar smoking products) in low-income neighborhoods compared to other types of neighborhoods. CRC's research question is, "Do low-income neighborhoods have more vape/smoke shops than other types of neighborhoods?" Low-income neighborhoods were defined as those where the median household income is less than the U.S. federal poverty line. Non-low-income neighborhoods are those that the median household income is greater than the U.S. federal poverty line.

CRC employed a team of undergraduate researchers to go out and count the number of vape/smoke shops in a random selection of low-income and non-low-income neighborhoods. They define the population as all neighborhoods in King County.

They found a significant difference in the number of vape/smoke shops across neighborhoods. Specifically, low-income neighborhoods had a greater number of vape/smoke shops compared to non-low-income neighborhoods.

1. Using an independent samples t-test, CRC compared his sample values of ____________ against the average of non-low-income neighborhoods.

A. Average number of vape/smoke shops in low-income neighborhood

B, Average budget for vape/smoke products spent on average per household

C. Likelihood of people vaping/smoking in low-income neighborhoods

D. Number of households within each neighborhood

2. Match the variables in the scenario above with the appropriate level of measurement.

Neighborhood type (i.e. Low-Income vs. Non-low-income neighborhoods)

      [ Choose ]            Ordinal            Interval/Ratio            Nominal      

Number of vape/smoke shops

      [ Choose ]            Ordinal            Interval/Ratio            Nominal      

3. A one-sample z-test examines the value of the sample average on some dependent variable (in the scenario above, number of vape/smoke shops) against the population average of the same variable.

True OR False

A manufacturer of electric lamps is testing a new production method that will be considered acceptable if the lamps produced by this method result in a normal population with an average life of 2,400 hours and a standard deviation equal to 300. A sample of 100 lamps produced by this method has an average life of 2,320 hours. Can the hypothesis of validity for the new manufacturing process be accepted with a risk equal to or less than 5%?

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.

A single thermometer is randomly selected and tested. Let ZZ represent the reading of this thermometer at freezing. What reading separates the highest 23.64% from the rest? That is, if P(z>c)=0.2364P(z>c)=0.2364, find c.

An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic.

Step 2 of 2:

Suppose a sample of 1453 new car buyers is drawn. Of those sampled, 363 preferred foreign over domestic cars. Using the data, construct the 99% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.

Lower Endpoint:

Upper Endpoint:

To determine the effectiveness of learning a cartwheel by watching a video, a gymnastics teacher randomly divided 15 novice gymnasts into 3 groups of 5 students each. One group (control) viewed a live demonstration of a cartwheel one time and then was tested. A second group (video) watched a video of a cartwheel 10 times, and then was tested. The third group (live) watched 10 live demonstrations of a cartwheel and then was tested. All 15 subjects were ranked on their ability to perform the cartwheel with the following results (1 is the highest rank, 15 is the lowest rank).

1. Test to see if there are significant differences in the group’s ability to perform the cartwheel.

2. If significant results are found, perform all 3 post-hoc tests and write up the conclusion for each. Which group performed the best?

how can you use regression analysis to make a decision as a cashier? Include a description of the decision, what would be the independent and dependent variables, and how data could ideally be collected to calculate the regression equation.

In a study at a large hospital the researcher wants to assure that male nurses are adequately represented. At this hospital 5% of the nurses are male. The researcher separates the nurses into female and male hats. He draws 95 female names and 5 male names. This is an example of:

Select one:

a. Simple random sampling.

b. Stratified random sampling.

c. Multistage random sampling.

d. Cluster sampling.

The average income of 16 families who reside in a large city is $54,356 and the standard deviation is $8256. The average income of 12 families who reside in a suburb of the same city is $46,512 with a standard deviation of $1311. At ? = 0.01, can it be concluded that the income of the families who reside within the city is greater than that of those who reside in the suburb? Assume the populations have equal variances and use the p-value method.

1. Develop the least squares estimated regression equation.  (to 3 decimals)

2. Suppose Wells Fargo Investments developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of 2.2 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?

   (to 3 decimals)

Question 10.1 (1 point) Suppose that the distribution of income in a certain tax bracket is approximately normal with a mean of $53,183.88 and a standard deviation of $1,799.608. Approximately 18.56% of households had an income greater than what dollar amount? Question 11 options: 1) We do not have enough information to calculate the value. 2) 54,793.14 3) 51,574.62 4) 2,842,851 5) 2,949,219 Question 12 (1 point) According to a survey conducted by Deloitte in 2017, 0.4609 of U.S. smartphone owners have made an effort to limit their phone use in the past. In a sample of 89 randomly selected U.S. smartphone owners, what is the probability that greater than 46 will have attempted to limit their cell phone use in the past? Question 10.2 options: 1) 0.0241 2) 0.1703 3) 0.8779 4) 0.0483 5) 0.1221 Question 10.3 (1 point) According to a survey conducted by Deloitte in 2017, 0.4702 of U.S. smartphone owners have made an effort to limit their phone use in the past. In a sample of 54 randomly selected U.S. smartphone owners, what is the probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past? Question 13 options: 1) 0.1383 2) 0.7244 3) 0.2756 4) 1.0844 5) 0.0132 Question 10.4 (1 point) According to a survey conducted by Deloitte in 2017, 0.44 of U.S. smartphone owners have made an effort to limit their phone use in the past. In a sample of 87 randomly selected U.S. smartphone owners, approximately __________ owners, give or take __________, will have attempted to limit their cell phone use in the past. Assume each pick is independent. Question 14 options: 1) 4.63 , 38.28 2) 38.28 , 21.40 3) 87 , 4.63 4) 38.28 , 0.44 5) 38.28 , 4.63