**INTRODUCTION: **Two indispensable statistical decision-making tools for a single

parameter are

- Hypothesis tests to investigate theories about parameters.

KNOWN SIGMA

**CONFIDENCE INTERVALS**

As an introduction, let’s follow Example 8.4 in your text.

Begin a new worksheet and generate 40 random integers the range 0 to 9 in column A. Use the Random Number Generation tool of Excel and then use the INT (integer) function to transform to integers in the range 0 to 9:

Choose: **Data > Data Analysis > Random Number Generation > OK**

Enter: Number of Variables: **1**

Number of Random Numbers: **40**

Select: Distribution: **Uniform**

Enter: Parameters, Between **0** and **10**

Output Range: **B1 > OK**

Enter: in cell A1: **=INT(B1)**

Click and drag: lower right corner to cell A40

To see the mean, standard deviation and maximum and minimum values for the data set use: Select: **Data > Data Analysis > Descriptive Statistics > OK**

Enter input and output range as appropriate, and select Summary Statistics

Find the 90% confidence interval for the mean of these values we generate in column A: Choose: **Data > Data Analysis Plus**** **>** **Z-Estimate: Mean** **> OK**

Enter: Input Range: **A1:A40**

Standard Deviation (SIGMA): **2.87 > OK**

Alpha: **.10 > OK**

So the 90% confidence interval for the mean is to . ** If “Data Analysis Plus” does not show on the File menu:

Save and Close your excel file

Open: __http://www.kellerstatistics.com/KellerStatistics/DataAnalysisPlus__ Click on: “Download DAPv9” bottom (Mac or Windows)

Save the file > Extract it > open it > double click on Excel file:“Stats_2007-2013_v9b” > Click on “__E__nable Macros” > Find “Data Analysis Plus” in “__Add-Ins__” at the menu toolbar of present Excel file > Reopen your previous excel file by dragging inside of present Excel file.

**HYPOTHESIS TESTING**

A standard final examination in an elementary statistics course is designed to produce a mean score of 75 and a standard deviation of 12. The hypothesis you will try to verify is: “This particular statistics class is above average.” At the .05 level of significance, test the claim that the following sample scores reflect an above-average class (assuming sigma = 12):

79 79 78 74 82 89 74 75 78 73 74 84 82 66 84 82 82 71 72 83

Test the hypothesis, “The mean test grade for this class is greater than 75.” Choose: **Add-Ins > Data Analysis Plus >** **Z-Test: Mean** **> OK**

Enter: Input Range: **A1:A20 or select cells > OK**

Hypothesized mean: **75**

Standard Deviation (SIGMA): **12 > OK**

Alpha: **.05 > OK**

Questions:

- What are the formal null and alternative hypotheses?

- What is the value of the test statistic, and what is your decision? Is the mean of this class above “average”?

UNKNOWN SIGMA

**THE CONFIDENCE INTERVAL**

To generate a confidence interval using the t-statistic we use Inference about a Mean command, specifying the level of confidence and the column of data for which the estimation is being made.

Consider the data presented in exercise 9.31[EX09-031] of your text. Open the data file. Before we complete a 95% confidence interval estimate for the mean length of lunch breaks

at Giant Mart, we check the normal probability plot and boxplot to verify the normality assumption.

Excel uses a test for normality (**Chi-Squared Test of Normality)**, not the probability plot. Choose: **Add-Ins > Data Analysis Plus > Chi-Squared Test of Normality > OK**

Enter: Input Range: **select cells**

Select: **Labels** (if column heading was used) **> OK**

*** IF **P***-value** greater the .05, given distribution is approximately normal.

To complete a 95% confidence interval estimate for the mean length of lunch breaks at Giant Mart complete the following steps:

Choose: **Add-Ins > Data Analysis Plus >** **t-Estimate: Mean** **> OK**

Enter: Input Range: **A1:A22**

Enter: Alpha: **.05 > OK**

With 95% confidence we estimate the mean length of lunch breaks at Giant Mart to be between and minutes.

**THE T TEST**

Using text exercise 9.29 [EX02-177] as the basis of our discussion, open the data file. Suppose we have been asked to determine whether this accelerator has decreased the drying time by significantly more than 4% at the 0.01 level.

To perform the test, use the following commands:

Choose: **Add-Ins > Data Analysis Plus >** **t-Test Mean** **> OK**

Enter: Input Range: **A2:A9 > OK**

Hypothesized mean: 4 Alpha: 0.01 **> OK**

Question:

- What are the formal null and alternative hypotheses?

- Is there sufficient evidence to show that this accelerator has decreased the drying time significantly more than 4% at the .01 level?