(due Friday May 4)

Confidence Intervals and Hypothesis Tests

Minitab Assignment 5: Confidence Intervals and Hypothesis Tests

Your Name

PROBLEM 1: Large Sample Confidence Interval

In this exercise we generate a 95% confidence interval for the population mean based on some canned data in Minitab. We use File > Open Worksheet,

then click on the datafile Plating, and open it. This stores 30 sample numbers from the Plating data file into column C1.

Next we apply Stat > Basic Statistics > Display descriptive statistics,

click Graphs, click Graphical Summary, ok ok. This produces a graph, which we print out using

File > Print graph.

< Print out the graph! It contains numerical statistics in addition to the pictures. >

The confidence interval produced by Minitab comes from the following formula:

< In your session window: type in the general formula which determines the 95% confidence interval Minitab produced for the mean. Then say what numbers are substituted for the general terms of your formula. Privately (not in the session window), check the arithmetic to be sure you are right. If you get a result which is a little different than what you expect -- see if you can explain the difference. >

PROBLEM 2: Large Sample Hypothesis Test for the Mean

Now we run a hypothesis test on this same plating data, at level of significance alpha = .05, for

H_1: mean > 3.0

H_0: mean = 3.0

For this we use Stat > Basic Stat > 1-sample Z

and in the resulting box put in the information corresponding to this test: variables C1, test mean 3.0, alternative greather than, type in st.dev. = 3.042, ok.

< That number 3.042 is the sample standard deviation for this data. You will get output in your session window. After the output, type your conclusion (the data do or do not support alternate hypothesis at this level alpha =.05); state the P-value; and in your own words explain the meaning of the P-value. >

PROBLEM 3: Small Sample Confidence Interval

We are going to use problem 17 of chapter 9 (see page 390 of the text).

We will get a 95% confidence interval for the density of the earth (water has density 1) using the the data given in Problem 17, collected by Henry Cavendish in 1798.

First, we clear C1 entries and then type into C1 the 23 numbers from that problem 17.

< Doublecheck your typing! Your answer must be correct.>

Then we get your 95% CI with Stat > Basic Statistics > 1-sample t, typing C1 in the Variables box, OK.

This confidence interval produced by Minitab comes from the following formula:

< In your session window: type in the general formula which determines the 95% confidence interval Minitab produced for the mean. Then say what numbers are substituted for the general terms of your formula. For one of these numbers you will have to use the t-table in the back of our text. Privately (not in the session window), check the arithmetic to be sure you are right. >

PROBLEM 4: Small Sample Hypothesis Test

Still using the data in C1, we will do a t-test for the claim that the mean of the earth is not equal to 5. , at level of significance alpha = .05 .

< Type into the session window the appropriate null hypothesis H_0 and the appropriate alternate hypothesis H_1. Then run the test, which proceeds as the large sample z-test above did, except that you choose "1-sample t-test" instead of "1-sample z-test", you use the not-equal rather than the greater than test, and you don't have to specify the standard deviation. After the output, type your conclusion. Then state the reported P-value (it should be 0.0000) and explain the meaning of this P-value. >