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A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years ago. Five years ago, a sample of 270 students showed that 120 considered themselves overweight. This year a poll of 300 students showed that 140 considered themselves overweight. At a 5% level of significance, test to see if there is any difference in the proportion of college students who consider themselves overweight between the two polls. What is your conclusion?

Respuesta :

Answer:

At 5% significance level, it is statistically evident that    there is nodifference in the proportion of college students who consider themselves overweight between the two poll                                  

Step-by-step explanation:

Given that a poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years ago.

Let five years ago be group I X and as of now be group II Y

[tex]H_0: p_x =p_y\\H_a: p_x \neq p_y[/tex]

(Two tailed test at 5% level of significance)

                Group I            Group II              combined p

n                  270                 300                         570

favor            120                  140                          260

p                   0.4444            0.4667                   0.4561

Std error   for differene = [tex]\sqrt{\frac{0.4561(1-0.4561)}{570} } \\=0.0209[/tex]

p difference = -0.0223    

Z statistic = p diff/std error =       -1.066

p value =0.2864

Since p value >0.05, we accept null hypothesis.

        At 5% significance level, it is statistically evident that    there is nodifference in the proportion of college students who consider themselves overweight between the two poll                                  

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