# Probability, sample size, type of error, confidence interval

1. Suppose you time how long it takes every student to complete this test, and assume that the results have a normal distribution with a mean of 120 minutes, and a standard deviation of 30 minutes. Let X be the time it will take you to complete the test.

a. What is the probability that X is between 100 and the mean?

b. Find P(X>180).

2. List and describe the 4 factors that are considered when determining sample size.

3. If we reject the null when it is actually true, we have made what type of error?

4. What is: Ho: μ=0; Ha: μ 0?

5. What does a 90% confidence interval tell us?

6. Calculate a 99% confidence interval for using a t distribution with the following information: sample mean = 4.5, sample standard deviation = .8, n = 23.

7. A college senior decides she wants to buy a condo. She knows she wants to live in an downtown neighborhood, but needs to investigate if that is feasible. She does some research and determines the average price per square foot in her preferred neighborhood for condos is $60.20 per square foot. The standard deviation is $10.34. She is assuming the square footage rates follow a normal distribution. The sample size was 54. Alpha is .05. The college senior believes that is she picks any random condo, she'll probably have to pay at least $65 per square foot or more. Does the statistical evidence support her belief (be sure to state your hypothesis and write out your work)?

8. When would a person decide to use a Poisson distribution to determine the probability of an event? (give an example)

9. Before launching a new video game production venture, you wish to study the expenditure of the average teenager in video games per year. You know that some kids don't play video games at all (expenditure of 0), while, from a recent news article, you know that the kid who set a record last year spent all of his allowance on video games, totaling $ 500 during the year (which gives you the range for your study). If you want the error of your estimate to be $10 or less, and a 95% confidence level, what size should your sample be? (Hint: in this case the standard deviation must be estimated)

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#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.

Confidence Interval, Sample Size and Type I Error

1. If the level of confidence is decreased from 95 percent to 90 percent, but the allowable error and the standard deviation remain the same, the required sample size for determining the confidence interval will be:

a. increased.

b. decreased.

c. unchanged.

2. The probability of committing a type I error is

a. equal to the probability of accepting Ho when Ho is true

b. equal to the probability of committing a Type II error

c. equal to the probability of accepting H1 when it is false

d. equal to the probability of rejecting Ho when Ho is true