Question

Write the equation used for…

Binomial Probability Formula:

Confidence interval for a proportion:

Confidence interval for a mean:

Test statistic for testing proportions:

Test statistic for testing means:

Symbols and Equations

Write the correct symbol for each term

Sample mean:

Sample proportion:

Sample size:

Sample standard deviation:

Population proportion:

Population mean:

Population standard deviation:

Confidence Intervals *Week 10

1. On my recent trip to space I observed the heights of 50 aliens. I found the average height to be 48 inches with a standard deviation of 9 inches. Find the 95% confidence interval for the true average height of aliens. Interpret the interval.

2. Of those 50 aliens 16 were green, and the rest were purple. Find and interpret the 95% confidence interval for the true proportion of aliens who are purple

Binomial Probability

What are the 4 requirements to be able to use the binomial probability formula?

3. Suppose I have 4 marbles in a bag, one red, one blue, one green, one yellow. My experiment consists of me randomly selecting one of the marbles, recording its color, then returning the marble to the bag. I will repeat this for a total of 5 observations. What is the probability that I select a red marble twice?
   1. Find n, x, and the probability of selecting a red marble

2. Use the binomial probability formula to find the probability that I select a red marble twice

3. Find the standard deviation

Answer 1

Let us answer this question

On my recent trip to space I observed the heights of 50 aliens. I found the average height to be 48 inches with a standard deviation of 9 inches. Find the 95% confidence interval for the true average height of aliens. Interpret the interval.

The number of aliens is given to be 50,

The average height is found to be 50. That is, and standard deviation is given by,

At 95% confidence level,

The 95% confidence interval of the true average is given by,

Therefore, we can say that we are 95% confident that the true average height of aliens lie between 45.51 and 50.51.