Statistics Through Applications
2nd Edition
ISBN: 9781429219747
Author: Daren S. Starnes, David Moore, Dan Yates
Publisher: Macmillan Higher Education
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Chapter 10.1, Problem 10.12E
To determine
To Explain: a significance test of the hypothesis that this program yields an equal proportion of 1s, 2s, 3s and 4s.
Expert Solution & Answer
Answer to Problem 10.12E
P<0.05⇒Fail to reject H0
There is not enough evidence to reject the claim that the digits were randomly selected.
Explanation of Solution
Given:
n=200
Formula used:
x2=∑(O−E)2E
Calculation:
Assume:
α=0.05
One of the four regions is arbitrary chose, and then every of the 4 regions requires to have 1 chance in four to be selected.
p=14=0.25
The null hypothesis statement is the population proportions are equal to the given proportions:
H0:p0=p1=p2=p3=p4=14=0.25
The alternative hypothesis statement is the opposite of the null hypothesis:
H1:At least one of the pi's is different.
Randomly generating the sample
A possible result is then in brief
| Region | Observed Frequency O |
| 1 | 49 |
| 2 | 50 |
| 3 | 47 |
| 4 | 54 |
GOODNESS OF FIT TEST
The multiplication of the sample size and the probabilities is the expected frequencies are
E1=np1=200×0.25=50E2=np2=200×0.25=50E3=np3=200×0.25=50E4=np4=200×0.25=50
The value of the test- statistic is
χ2=∑(O−E)2E=(49−50)250+(50−50)250+(47−50)250+(54−50)250=0.52
The degree of freedom is the number of variables decreased by 1.
df=c−1=4−1=3
The P-Value is the probability of obtaining the value of the test statistic, or value more extreme. The P-value is the number in the column of the chi-square distribution containing the x2 -value in the row df=c−1=4−1=3:
P>0.25
If the P-value is equal or less than to the significance level, then the Alternate hypothesis is accepted and null hypothesis is rejected:
P>0.05⇒Fail to reject H0
There is no enough evidence to reject the claim that the digits were randomly selected.
Chapter 10 Solutions
Statistics Through Applications
Ch. 10.1 - Prob. 10.1ECh. 10.1 - Prob. 10.2ECh. 10.1 - Prob. 10.3ECh. 10.1 - Prob. 10.4ECh. 10.1 - Prob. 10.5ECh. 10.1 - Prob. 10.6ECh. 10.1 - Prob. 10.7ECh. 10.1 - Prob. 10.8ECh. 10.1 - Prob. 10.9ECh. 10.1 - Prob. 10.10E
Ch. 10.1 - Prob. 10.11ECh. 10.1 - Prob. 10.12ECh. 10.1 - Prob. 10.13ECh. 10.1 - Prob. 10.14ECh. 10.1 - Prob. 10.15ECh. 10.1 - Prob. 10.16ECh. 10.1 - Prob. 10.17ECh. 10.1 - Prob. 10.18ECh. 10.1 - Prob. 10.19ECh. 10.1 - Prob. 10.20ECh. 10.1 - Prob. 10.21ECh. 10.1 - Prob. 10.22ECh. 10.1 - Prob. 10.23ECh. 10.1 - Prob. 10.24ECh. 10.1 - Prob. 10.25ECh. 10.1 - Prob. 10.26ECh. 10.1 - Prob. 10.27ECh. 10.1 - Prob. 10.28ECh. 10.1 - Prob. 10.29ECh. 10.1 - Prob. 10.30ECh. 10.1 - Prob. 10.31ECh. 10.1 - Prob. 10.32ECh. 10.2 - Prob. 10.33ECh. 10.2 - Prob. 10.34ECh. 10.2 - Prob. 10.35ECh. 10.2 - Prob. 10.36ECh. 10.2 - Prob. 10.37ECh. 10.2 - Prob. 10.38ECh. 10.2 - Prob. 10.39ECh. 10.2 - Prob. 10.40ECh. 10.2 - Prob. 10.41ECh. 10.2 - Prob. 10.42ECh. 10.2 - Prob. 10.43ECh. 10.2 - Prob. 10.44ECh. 10.2 - Prob. 10.45ECh. 10.2 - Prob. 10.46ECh. 10.2 - Prob. 10.47ECh. 10.2 - Prob. 10.48ECh. 10.2 - Prob. 10.49ECh. 10.2 - Prob. 10.50ECh. 10.2 - Prob. 10.51ECh. 10.2 - Prob. 10.52ECh. 10.2 - Prob. 10.53ECh. 10.2 - Prob. 10.54ECh. 10.2 - Prob. 10.55ECh. 10.2 - Prob. 10.56ECh. 10.2 - Prob. 10.57ECh. 10.2 - Prob. 10.58ECh. 10 - Prob. 10.59RECh. 10 - Prob. 10.60RECh. 10 - Prob. 10.61RECh. 10 - Prob. 10.62RECh. 10 - Prob. 10.63RECh. 10 - Prob. 10.64RECh. 10 - Prob. 10.65RECh. 10 - Prob. 10.66RECh. 10 - Prob. 10.67RECh. 10 - Prob. 10.68RE
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