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?

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)

Solution Summary

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

Construct a graph determining the probability for the following problems. The sample mean and sample standard deviation are present. Construct a 90% confidenceinterval using the population mean and sample size.

Discuss what happens to the width of the confidenceinterval as the sample size is decreased. Discuss what happens to the width of the confidenceinterval as the confidence level is increased. Is this reasonable? Explain.

Problem 3
a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidenceinterval estimate of the population mean.
b. Repeat part (a) with a sample size of 100.
c. Repeat part (a) with a sample size of 400.
d. Describe what happens to the conf

Please help with the following problems.
1. For df = 25, determine the value of A that corresponds to each of the following probabilities:
a.P(t > A) = 0.25
b. P( < A) = 0.10
c. P(-A < t < A) = .99
2. Given the following observations in a simple random sample from a population that is approximately normally distrib

3. in an effort to estimate the annual income for new graduates, data were collected from 500 new graduates over a one -year period. assume a population standard deviation of $500.
a) if the sample mean is $15,000, what is the 95% confidenceinterval for the population mean?
b) if the sample mean is $15,000, what is the 98

8.4. What are the five steps to create a confidenceinterval for a z distribution?
8.6. What effect does increasing the sample size have on the standard error and the test statistic for every hypothesis test?
8.8. What does it mean to say the effect-size statistic, such as Cohen's d, neutralizes the influence of sample siz

You are constructing a 95% confidenceinterval using the information: n = 60, = 65.5, s = 2.5, and E = 0.7. What is the value of the middle of the interval?
A. 0.7
B. 2.5
C. 0.95
D. 65.5
What sample size would be needed to estimate the population mean to within one-half standard deviation with 95% confidence?

Given the following information, calculate a confidenceinterval using a 95 percent confidence level: sample proportion =.4, standard error of the proportion =.05, and sample size =100.

I need help solving 95% confidenceinterval and point estimate problems.
A sample of 16 people are used, each one is to keep track of their time with the following result in hours.
1.8, 1.7, 0.9, 1.1, 1.5, 1.5, 1.2, 0.6, 1.4, 0.9, 0.7, 1.8, 1.7, 2.2, 1.5, 1.3
Construct a 95% confidenceinterval for the amount of time n

1.Which of the following statements about the sampling distribution of the sample mean is incorrect?
a. The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n>30).
b. The sampling distribution of the sample mean is generated by repeatedly taking samples of size n