A random sample of 150 smokers from five different age groups produces the given

Question

A random sample of 150 smokers from five different age groups produces the given data given below. At the .01 significance level test the claim that the proportion of smokers in each age group is the same Age: 20-24 25-34 35-44 45-64 65 and over. Number: 36 32 35 31 16

(a) State the null hypothesis tested above

(b) What are the expected frequencies

(c) What is the computed x^2 value

(d) What is the tabled x^2 value

(e) What decision will you make about null hypothesis (accept or reject)

(f)What does this decision mean in terms of the experiment

(g) What type of error is possible?

Explanation / Answer

(a) Null hypothesis : All groups have same frequencies

(b) There are 5 groups and a total of 150 frequencies,thus the number of expected frequencies for each group is 30.

(c)

Thus the chi-square value is 8.73.

(d) At 0.01 significance level with 4 degrees of freedom, the tabled chi-square value is found to be 7.80

(e) Since tabled value is smaller than computed value, we reject the null hypothesis.

(f) Proportion of smokers in each group is not same.

(g) We are not sure if only group has different proportion or more than one group.

Age Observed frequency (O) Expected frequency(E) (O-E)2/E 20-24 36 30 1.20 25-34 32 30 0.13 35-44 35 30 0.83 45-64 31 30 0.03 65 and over 16 30 6.53 Chi-square 8.73

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