How many simple random samples of 12 elements can be taken from a  population containing 67 elements?

A teacher wants to interview a random sample of 6 students from their class of 25 students. How many samples (or groups) of 6 students can the teacher interview? Is this a combination or permutation? How many different possible samples are there?

A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 124 people living in Gastown and finds that 25 have an annual income that is below the poverty line.   Part i) The proportion of the 124 people who are living below the poverty line, 25/124, is a:   A. statistic. B. variable of interest. C. parameter. Part ii) Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line.   (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).   95% confidence interval = (    ,     )

Suppose Kathy bought a large bag of candy that comes in 4 flavors: cherry, strawberry, orange, and lemon. Out of the 84 pieces of candy 23 were cherry, 24 were strawberry, 21 were orange, and 16 were lemon. Kathy performed a chi-square GOF test to determine if the flavors were evenly distributed. What flavor contributed the most to the chi-square test statistic?

In order to conduct an experiment,  5 subjects are randomly selected from a group of 43 subjects.  How many different groups of 5 subjects are possible.

Sleep researchers were trying to understand the impact of cell phone use before bedtime on the amount of time it took a person to fall asleep. Using a matched pairs design, they chose 8 subjects and recorded the amount of time it took the subject to fall asleep, both when using the cell phone up to attempting to sleep and stopping using the cell phone 2 hours prior to attempting to sleep, in random order. The amount of time for each person for each attempt is recorded in the table below. Person                 1   2   3   4  5   6   7    8Until Attempt     22 17 45 15 35 19 36 18Two Hours Prior 18 18 40  8  23 15 32 12Difference a. Compute the difference for each observation.b. Based on the above data compute the mean and sample standard deviation of the difference.

In order to conduct an experiment, 4 subjects are randomly selected from a group of 47 subjects. How many different groups of 4 subjects are possible? The number of possible different groups is. (Type a whole number.)

ou have 2 six sided dice and you want to know how often and what percentage of each combination is rolled for a designated number of rolls. Ask the user how many times they want to roll the 2 dice. Use the random number generator to produce 2 numbers in the range of 1-6. This will simulate each dice. For output, show what each dice was for each roll (Use a loop to do this) and then print a summary report of how many of each total you rolled. The summary report will show how many rolls were made, how many of each total (remember totals will be 2 - 12) and what percentage each total was from all the rolls (number of that total/total rolls *100). Example Below. Be sure to ask the user if they would like to run the program again (Hint: Be sure to carefully place your play again while loop so that all the counters can be reset to 0 to play the game again. Summary report: Number of Total Rolls of the Dice: 500 Sum of Two Dice Number Percentage 50 10% 100 20% 12 1%

Suppose we have a set of 37 lightbulbs, and we wish to select a random sample of 5 distinct bulbs from this set. How many possible such samples exist? There are possible samples of this size.

A car dealer is interested in comparing the average gas mileages of four different car models. The dealer believes that the average gas mileage of a particular car will vary depending on the person who is driving the car due to different driving styles. Because of this, he decides to use a randomized block design. He randomly selects five drivers and asks them to drive each of the cars. He then determines the average gas mileage for each car and each driver. Can the dealer conclude that there is a significant difference in average gas mileages of the four car models? The results of the study are as follows.  Average Gas Mileage Driver Car A Car B Car C Car D Driver 1 3232 2222 3030 3939 Driver 2 2121 3939 3838 3737 Driver 3 2626 3131 3232 3939 Driver 4 3838 4040 2323 3434 Driver 5 3131 2929 2121 2222 Copy Data ANOVA Source of Variation SSSS dfdf MSMS Rows 174.2000174.2000 44 43.550043.5500 Columns 91.600091.6000 33 30.533330.5333 Error 607.4000607.4000 1212…