In: Statistics and Probability
Use the following information to answer the next questions: We
are interested in whether this age group of males fits the
distribution of the U.S. adult population. Calculate the frequency
one would expect when surveying 400 people.
Observed Values: Never married 150; Married 228; Widowed 5;
Divorced/Separated 17
Expected Values follow these proportions: Never married 30%;
Married 56%; Widowed 3%; Divorced/Separated 11%
What test are you running?
What is the observed values for never married?
What is the observed values for married?
What is the observed values for widowed?
What is the observed values for divorced/separated?
What is the expected values for never married?
What is the expected values for married?
What is the expected values for widowed?
What is the expected values for divorced/separated?
What are the degrees of freedom?
What is the null hypothesis?
What is the alternative hypothesis?
What is the test statistic? Use one decimal place.
What is the p-value? Use three decimal places.
What is your conclusion based on the p-value and the level of significance?
At the 5% significance level, what can you conclude?
What test are you running? :Chi square goodness of fit test:
What is the observed values for never married?=150
What is the observed values for married?=228
What is the observed values for widowed?=5
What is the observed values for divorced/separated?=17
What is the expected values for never married?=np=400*0.3 =120
What is the expected values for married? =400*0.56=224
What is the expected values for widowed?=400*0.03 =12
What is the expected values for divorced/separated?=400*0.11=44
degree of freedom =categories-1= | 3 |
null hypothesis:Ho: age group of males fits the distribution of the U.S. adult population
Alternate hypotheiss: Ha: age group of males does not fits the distribution of the U.S. adult population
applying chi square goodness of fit test: |
relative | observed | Expected | residual | Chi square | |
category | frequency(p) | Oi | Ei=total*p | R2i=(Oi-Ei)/√Ei | R2i=(Oi-Ei)2/Ei |
1 | 0.300 | 150.000 | 120.00 | 2.74 | 7.500 |
2 | 0.560 | 228.000 | 224.00 | 0.27 | 0.071 |
3 | 0.030 | 5.000 | 12.00 | -2.02 | 4.083 |
4 | 0.110 | 17.000 | 44.00 | -4.07 | 16.568 |
total | 1.000 | 400 | 400 | 28.2229 | |
test statistic X2 = | 28.2229 | ||||
p value = | 0.0000 |
since p value <0.05 , we reject null and conclude that age group of males does not fits the distribution of the U.S. adult population