Question

mong the literature on quitting smoking are data detailing the relative successfulness of people of different ages in quitting smoking. a study of 400 adults wh began various smoking cessation programs produced the data in the table below. in the table, each participant is classified according to two variables: length o their smoking cessation period (\less than two weeks\, \between two weeks and one year\, or \at least one year\) and age (\21 - 34\, or \35 and over\). in the table, \less than two weeks\ means that the individual returned to smoking within two weeks of beginning the program; \between two weeks and one year\ means that the individual lasted the first two weeks without smoking but retuned to smoking within a year; and \at least one year\ means that the individual has not smoked for at least a year since beginning the program. the table is a contingency table whose cells contain the respective observed frequencies of classifications of the 400 smokers. in addition, three of the cells have blanks beneath the observed frequencies. fill in these blanks with the frequencies expected if the two variables, age and length of the smoking cessation period, are independent. round your answers to two or more decimal places. send data to excel length of smoking cessation period less than two weeks between two weeks and one year at least one year total 21 - 34 69 133 38 240 age 35 and over 34 77 49 160 total 103 210 87 400

Explanation:

Step1: Calculate row total for 21-34

Sum observed values: $69 + 133 + 38 = 240$

Step2: Calculate column totals

• Less than two weeks: $69 + 34 = 103$
• Between two weeks and one year: $133 + 77 = 210$
• At least one year: $38 + 49 = 87$

Step3: Compute expected frequency for 21-34 & <2 weeks

Formula: $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$
$\frac{240 \times 103}{400} = 61.80$

Step4: Compute expected frequency for 21-34 & between

$\frac{240 \times 210}{400} = 126.00$

Step5: Compute expected frequency for 35+ & at least one year

$\frac{160 \times 87}{400} = 34.80$

Answer:

61.80, 126.00, 34.80