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[answered] Math 215 - Statistical Concepts Franklin University HOW &am

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Math 215 ? Statistical Concepts Franklin University HOW ?FIT? IS YOUR DATA SET?

Problem I: How random are your numbers? In this activity, find a friend, a family member or a class mate and ask them to give you a list of

100 random digits (ranging from 0 to 9) from their head without the use of a calculator,

computer or a printed random table numbers. (3 4 4 2 1 6 4 8 9 0 7 8 6 5 5 5 2 1 2 3

?. etc)

Then make a frequency table to determine how many times each digit is listed. (This will be

your observed frequencies) You can use the following table for this purpose:

Digits

0

1

2

3

4

5

6

7

8

9

Total Observed

Frequency Expected

Frequency 100 100 1. Fill in the Observed Frequencies column in the table above, by counting how many times

each number occurs in your friend?s 100 random digit list.

2. If your friend?s random digits were really random (i.e. if each digit was equally likely to

appear on the list), how many of each digit should there be? Put these numbers in the

Expected Frequencies column.

3. If your friend?s random digits were really random, how do you think the Observed

Frequencies differ from the Expected Frequencies? Exactly equal? Close to each other?

Completely different?

4. Now, let?s conduct a statistical test to determine if your friend?s random digits have a

similar frequency distribution to what we would expect for true random digits. In other

words, conduct a test to see if the Observed Frequencies make a ?good enough fit? with

Expected frequencies in the table above, with the significance level of 0.05. If the

210515 1 Math 215 ? Statistical Concepts Franklin University frequencies are close to each other, then we can conclude that the digits were really

random. Follow the following steps:

i.

ii. State the hypotheses:

H0 :

H1 :

What statistical test can be used here? Determine if the conditions of the test

are satisfied. iii. Compute the test statistic and give your answer using the correct symbol. If

you use your calculator, give your calculator command; if you use the

formula, show your work. iv. What is the degrees of freedom? v. Find the critical value from a table using the degrees of freedom. vi. Make a decision as whether to reject the null hypothesis or not. vii. Interpret this decision in the context of the problem. Are your friend?s 100

random digits really random? Problem II: Who is more satisfied?

An urban economist wants to determine whether the region of the US a resident lives in is

associated with their general level of satisfaction with life. She randomly selects 100 residents

18 years of age or older from four geographic regions of the US: East, South, Midwest and West,

a total of 400 US adults. She asks: ?Are you generally satisfied or dissatisfied with the way things

are going in your life at this time?? She summarizes the results in the following table.

Satisfaction

Level

Satisfied

Dissatisfied East US Regions

South Midwest West 51

49 56

44 62

38 55

45 Perform a Test of Independence to determine whether geographic region a resident lives in and

their level of satisfaction with their life are associated. Use a significance level of 0.05. Follow

these steps:

i.

210515 State the hypotheses:

2 Math 215 ? Statistical Concepts Franklin University H0 :

H1 : 210515 ii. Find the expected frequencies for each cell in the table above. You may use

your calculator for this and just report the numbers here. iii. Compute the test statistic and give your answer using the correct symbol. If

you use your calculator, give your calculator command; if you use the

formula, show your work. iv. What is the degrees of freedom? v. Find the critical value from a table using the degrees of freedom. vi. Make a decision as whether to reject the null hypothesis or not. vii. Interpret this decision in the context of the problem. Is life satisfaction level

of residents associated with the geographic region they live in? 3

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