Mathematics College

2) In a random survey of 500 women, 315 said they would rather be poor and thin than rich and fat; in a random survey of 400 men, 220 said they would rather be poor and thin than rich and fat. Is there sufficient evidence to show that the proportion of women who would rather be poor and thin than rich and fat is greater than the proportion of men who would rather be poor and thin than rich and fat

Answers

Answer 1

Answer:

Since the calculated value of Z= 0.242887  is less than  Z (0.05) = 1.645 and falls in the critical region we  reject the null hypothesis and conclude that there is not sufficient evidence to show that the proportion of women who would rather be poor and thin than rich and fat is greater than the proportion of men who would rather be poor and thin than rich and fat.

Step-by-step explanation:

Here

p1= proportion of women who  would rather be poor and thin than rich and fat

p1= 315/500= 0.63

p2= proportion of men who  would rather be poor and thin than rich and fat

p2= 220/400= 0.55

1) Formulate the hypothesis as

H0: p1>p2   against the claim  Ha: p1 ≤ p2

2) Choose the significance level ∝0.05

3) The test Statistic under H0 , is

Z= p1^ - p2^ / sqrt( pc^qc^( 1/n1 + 1/n2))

pc^= an estimate of the common proportion

pc ^ = n1p1^ + n2p2^/ n1+n2

4) The critical region is Z≤ Z (0.05) = 1.645

5)  Calculations

pc^ = 315+ 220/ 500+400=  535/900

pc^= 0.5944

and qc^= 1-0.5944= 0.4055

Thus

Z = 0.63-0.55/ sqrt ( 0.5944*0.4055( 1/500+ 1/400))

Z= 0.08/ sqrt (0.24108 (900/2000))

Z= 0.08/√0.10849

Z= 0.242887

Conclusion :

Since the calculated value of Z= 0.242887  is less than  Z (0.05) = 1.645 and falls in the critical region we  reject the null hypothesis and conclude that there is not sufficient evidence to show that the proportion of women who would rather be poor and thin than rich and fat is greater than the proportion of men who would rather be poor and thin than rich and fat.

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