Question

In: Statistics and Probability

Use the following information to answer the next questions: We are interested in whether this age...

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?

Solutions

Expert Solution

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

orchestra answered 10 months ago
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