# Statistical Tests

I need to know the thinking process and how to solve the problem using Excel.

PART I: Is there a keyboard configuration that is more efficient than the one that most of us now use? The traditional keyboard configuration is called QWERTY (letters on the top of the row) it was designed to force people type slower to avoid machine jamming, The Dvorak keyboard supposedly provides a more efficient arrangement by positioning the most used keys on the middle row. In a magazine article that suggested that you can measure the ease of typing by using this point rating system: Count each letter on the middle row as 0, count each letter on the top row as 1, count each letter on the bottom row as 2, Using this rating system with each of the 52 words in the Preamble to the Constitution, we get the rating values shown below:

[see attachment]

Based on above info answer the following questions:

(a.) Using the given sample data with the methods from chapter seven, show that the Dvorak configuration has significantly lower ratings than the QWERTY, indicating that the Dvorak is easier to use. [Hint: use confidence intervals]

(b.) Is there anything about the rating system or the choice of words for the sample that might affect the conclusion about which keyboard configuration is easier to use?

(c.) Write a brief report of your findings and conclusions.

(d.) If the Dvorak keyboard is actually easier to use, why is it not being adopted by almost everyone who now uses a keyboard? How might that change?

PART II:

(1.) Below is a set of scores compiled from one particular on-line IQ test.

101, 93, 122, 88, 99, 96, 100, 127, 99, 93, 116, 162, 78,119, 83

(a) Using the IQ test data, test the hypothesis that the mean IQ is 100.

(b) Test the hypothesis that the standard deviation in IQ is 15 points. Summarize your results using a 0.05 level of significance.

(2.) In the last half of the 19th century, A.A. Michelson collected 100 experimental measurements of the speed of light through air. Modern day methods estimate the value Michelson should have observed to be 299,734.5 km/s (as opposed to the speed of light in a vacuum, which is accepted as 299,792.5 km/s.) Michelson's original measurements can be found by going to http://lib.stat.cmu.edu/DASL/Datafiles/Michelson.html. Note that 299,000 has been subtracted from each data point.

Formulate and conduct a hypothesis test that determines whether Michelson's speed of light measurements were in the ballpark of the true value. That is, that the set of 100 measurements reflects a true value of 299,734.5 km/s with measurement error.

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#### Solution Preview

See the attached Word document. I used Excel when possible, and I've included the Excel spreadsheets I used.

W3Part I

Is there a keyboard configuration that is more efficient than the one that most of us now use? The traditional keyboard configuration is called QWERTY (letters on the top of the row) it was designed to force people type slower to avoid machine jamming, The Dvorak keyboard supposedly provides a more efficient arrangement by positioning the most used keys on the middle row. In a magazine article that suggested that you can measure the ease of typing by using this point rating system: Count each letter on the middle row as 0, count each letter on the top row as 1, count each letter on the bottom row as 2, Using this rating system with each of the 52 words in the Preamble to the Constitution, we get the rating values shown below

QWERTY keyboard word rating for

Preamble to the Constitution.

2 2 5 1 2 6 3 3 4 2

4 0 5 7 7 5 6 6 8 10

7 2 2 10 5 8 2 5 4 2

6 2 6 1 7 2 7 2 3 8

1 5 2 5 2 14 2 2 6 3

1 7

Dvorak keyboard word rating for

Preamble to the Constitution.

2 0 3 1 0 0 0 0 2 0

4 0 3 4 0 3 3 1 3 5

4 2 0 5 1 4 0 3 5 0

2 0 4 1 5 0 4 0 1 3

0 1 0 3 0 1 2 0 0 0

1 4

Based on above info answer the following questions:

a. Using the given sample data with the methods from chapter seven, show that the Dvorak configuration has significantly lower ratings than the QWERTY, indicating that the Dvorak is easier to use. [Hint: use confidence intervals]

Here, we want to show that the average rating for the Dvorak is lower than the average rating for the QWERTY.

We know that the average rating for the words in the Preamble is 4.4 for QWERTY and 1.7 for Dvorak (see the Excel file). However, this is just a sample of words. Can we say that the average rating for all words is lower on the Dvorak? To estimate ...

Statistical Hypothesis Testing: Crusty The Clown' Cereal

1. The sales of Crusty The Clown cereal since 2000 are:

Year Code Sales

($ millions)

2000 1 5

2001 2 7

2002 3 6

2003 4 10

2004 5 12

What is the sales forecast for 2005?

2. The owner of a car dealership wants to determine whether there is a relation between the income level and the type of vehicle purchased in their dealership. He randomly sampled 500 car buyers and obtained the following data:

Income Level SUV/Minivan Midsize Compact

up to $30K/yr 13 71 106

$30K-$60K 33 76 45

more than $60K/yr 66 59 31

At the .05 level of significance, determine whether there is a relation between the income level and the type of vehicle purchased. Show your work step by step.

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