Inferential Statistics

Question description

These are the questions from my professor that I need to answer (minimum 100 words):

This week we will study Inferential Statistics including both Confidence Intervals and Hypothesis Testing.

1. Example Confidence Interval Problem- Example Exercise

A gasoline station owner wanted to estimate the mean number of gallons sold per customer. He selected a random sample of 60 customers and found a mean of 8.6, with a Standard Deviation of 2.3. What would be the 95% Confidence Interval for his sampling?

8.6 +/- 1.96 (2.3/)

= 8.6 +/- 1.96 (2.3/7.75)

= 8.6 +/- 0.58

= 8.02 to 9.18

So there is a 95% probability that the true mean of gallons purchased would be between 8.02 and 9.18. Why is this range so wide? The 2.3 gallon Standard Deviation found in the sample is large relative to the Mean and contributes to the range. You may want to use the t Statistic if you do not have the Population Standard Deviation for the problem.

2. Set Up One-Sample Hypothesis Test- We begin with One-Sample Hypothesis Testing. We have learned to set up the Null and Alternativehypothesis, then conduct a test. In research we use this process to test for significant differences or to test a claim made about the Population Parameter(s).

Discuss some data or claim you would like to test and set up the Null and Alternative hypothesis for it and tell how you would conduct the test using the Z statistic.

What do you expect to result from the test?

3. Z or t? The first hypothesis testing methods we study are the Standard Normal or Z and the Student’s t. The first statistic was discussed last week under Continuous Probabilities. You may want to compare and contrast these two distributions.

When do we use Z and when do we test with t?