An important step in creating confidence intervals for proportions is to check whether the success/failure conditions have been met otherwise the interval created will not be valid (i.e. we should not have created that interval)!

The following examples are estimating the proportion of the population who likes Brussels sprouts. Try to determine whether or not the assumptions have been met.

1. A class has 15 girls and 10 boys. The teacher wants to form an unordered pair consisting
of 1 girl and 1 boy. How many ways are there to form such a pair?

2. For the same setup (i.e. class of 15 girls and 10 boys), the teacher wants to form an
unordered group of 3, consisting of 2 girls and 1 boy. How many ways are there to form
such a group?

3. For the same setup (i.e. class of 15 girls and 10 boys), assume the teacher now wants to
form an ordered group of 3, consisting of 2 girls and 1 boy (e.g., think of each student
having a different task, so their order, i.e. who does what, matters). How many ways
are there to form such a group?

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 255 feet and a standard deviation of 37 feet. Let X be the distance in feet for a fly ball.

a. What is the distribution of X? X ~ N(___,__)

b. Find the probability that a randomly hit fly ball travels less than 278 feet.____ Round to 4 decimal places.

c. Find the 70th percentile for the distribution of distance of fly balls. Round to 2 decimal places. ___ feet

Fill in "___" please.

You are given a list of all employees. You group the names by department (Logistics, Sales, IT, Human Resource). Suppose you select all employees in Sales.

What type of sampling method did you use to select the employees? Explain your reasoning.

Im doing an econometric assignment and need to use the program STATA do estimate some linear regressions.

The dataset provided is the "natural log" of each variable.

What does the natural log mean? How is it calculated and how do I interoperate the data?

For example, a summary of the natural log of the unemployment rate shows:

Mean: -2.79

STD Deviation: 0.284

Min: -3.5833

Max: -1.9428

On average, indoor cats live to 15 years old with a standard deviation of 2.7 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(__,___)

b. Find the probability that an indoor cat dies when it is between 10.3 and 11.5 years old. ___

c. The middle 30% of indoor cats' age of death lies between what two numbers?
     Low: ____ years
     High: ____ years

Fill in the "___"

Suppose a fitness center has two weight-loss programs. Fifteen students complete Program A, and fifteen students complete Program B. Afterward, the mean and standard deviation of weight loss for each sample are computed (summarized below). What is the difference between the mean weight losses, among all students in the population? Answer with 95% confidence.

Prog A - Mean 10.5 St dev 5.6

Prog B - Mean 13.1 St dev 5.2

Applications that do not violate the OLS assumptions for inference. Identify the response and explanatory variable(s) for each problem. Write the OLS assumptions for inference in the context of each study.

1. Cricket Chirps. Researchers record the number of cricket chirps per minute and temperature during that time to investigate whether the number of chirps varies with the temperature.
2. Women’s Heights. A random selection of women aged 20-24 years are selected and their shoe size is used to predict their height

An article gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Here are the values of the variable x = total length of streets within a subdivision:

(a) Construct a stem-and-leaf display using the thousands digit as the stem and the hundreds digit as the leaf. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

What proportion of subdivisions have total length less than 2000? Between 2000 and 4000? (Round your answers to three decimal places.)

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components, 32% contain one defective component, and 18% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

(b) One of the two tested components is defective. [Hint: Draw a tree diagram with three first-generation branches for the three different types of batches.]

In 2017, 965 students registered for a course. Explain how you will use the random number table to select a simple random sample of 20 students.
Start from digit one of row 6.


Fill in the blanks
1. Bar chart is normally used for ___________ data.
2. Pie chart presents ___________ data.
3. A ____________________ is used to describe the relationship between two categorical variables.
4. A ___________ histogram is one with a single peak.
5. A ___________ histogram is one with two peaks.
6. Observations measured at the same point in time across individual units are called _______________ data.
7. Observations measured at successive points in time on a single unit are called _______________ data.

The mean of the uniform distribution between 0 and 1 is μ = 0.5. Estimate this value with a 95% confidence interval using samples of 100, 200, 400, 800, 1600, 3200, and 6400. Plot the confidence intervals using the computer and show graphically that the estimates converge to 0.5.

Can you show steps in excel or what should I put in column?

In a store, 40% of customers make a single purchase. This activity requires a time that has an exponential distribution with mean 2.0 minutes. The other 60% of customers ask for information before making a purchase. This process requires time and has a symmetric triangular distribution with between 1 and 5 minutes (in addition to the purchase time). Use Bernoulli, exponential and triangular random variates to generate a sample of shopping times for 200 customers. Plot the histogram of these observations.

Can you show steps in excel or what should I put in the column?

Does anyone know how to do it on EXCEL?

Does anyone know how to do it on EXCEL?

Does anyone know how to do it on EXCEL?

Does anyone know how to do it on EXCEL? Anyone know how to do it on EXCEL?

The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of fresh fruit per person is 99.9 pounds. The standard deviation of fresh fruit consumption is about 30 pounds. Suppose a researcher took a random sample of 38 people and had them keep a record of the fresh fruit they ate for one year.

a) What is the probability that the sample average would be less than 90 pounds?

b) What is the probability that the sample average would be between 98 and 105 pounds?

c) What is the probability that the sample average would be less than 112 pounds?

d) What is the probability that the sample average would be more than 93 pounds?