Question

According to a survey in PARADE magazine, almost half of parents say their children's weight is fine. Only 9% of parents describe their children as overweight.† However, the American Obesity Association says the number of overweight children and teens is at least 15%. Suppose that you sample n = 600 parents and the number who describe their children as overweight is x = 58.

(a)

How would you test the hypothesis that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Association? (Round your answers to two decimal places.)

State the null and alternative hypotheses. (Choose Correct Letter)

a) H₀: p ≠ 0.15 versus H_a: p < 0.15

b) H₀: p ≠ 0.09 versus H_a: p < 0.09

c) H₀: p = 0.09 versus H_a: p > 0.09

d) H₀: p = 0.15 versus H_a: p > 0.15

e) H₀: p = 0.15 versus H_a: p < 0.15

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statistic:   z=

rejection region: z>

z<

(b)

What conclusion are you able to draw from these data at the α = 0.05 level of significance? (Choose Correct Letter)

a) H₀ is not rejected. There is sufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.

b) H₀ is not rejected. There is insufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.    

c) H₀ is rejected. There is insufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.

d) H₀ is rejected. There is sufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.

(c)

What is the p-value associated with this test? (Round your answer to four decimal places.)

p-value =

Answer 1

a) Answer- here the total no of parents or samples =n= 600,

Number of parents who described their children as overweight= x=58

Under null hypothesis ho: p= 0.15 versus ha:p<0.15 so, correct option is (e).

Reason for choosing null and alternative hypothesis

We have to test the hypothesis that porportion of parents who described their children as overweight is less than the actual proportion reported by the American onesiob association.

We test this by using testbof significance of single proportion .

P= probability of success=x÷n= 58÷600 = 0.0967,and Q = 1-P= 0.9033

We have,

Z= (x-nP)÷√nPQ ~ N(0,1) , since, n is large

Now, Z= (58-600*0.0967)÷√600*0.0967*0.9034= - 0.02÷ 7.2394= -0.002762,

Most probable region is given by P^±1.645 √ P^Q^/n = 0.0968±0.0008102= (0.09588,0.0975) so, rejection region is z>0.09588 and z<0.0975

B) at 5% level of significance z = -1.645 ,for left tail test

And our calculated vale is - 0.002762 which is greater than tabulated value so,we reject ho at 5% level of significance.

So, correct option is (c)

C) answer- the p- value for z= -0.002762 is 0.499202