In a recent research study concerning nutrition, it was reported that only 2% of

Question

In a recent research study concerning nutrition, it was reported that only 2% of children in the United States ages 6-10 eat the recommended number of servings for all five major food groups each day. A certain state conducted a nutrition campaign through elementary schools, newspapers, and television. Following the campaign, a random sample of 500 children in this age group was obtained, and 16 were found to eat the recommended number of servings each day. a. Identify n, x, and p_0. b. Check the nonskewness criterion. Is a large-sample hypothesis test about p appropriate? c. Conduct the appropriate hypothesis test to determine whether the proportion of children who eat the recommended number of servings each day has increased Use alpha = 0.05. d. Compute the p value associated with this test.

Explanation / Answer

a. n = 500 , x = 16 and p0= 0.02 and p = 16/500 = 0.032

b. non skewness criteria

np >= 10 => 500 * 0.032 = 16>= 10

and n(1-p) >= 10 => 500* ( 1 - 0.032) = 484 >=10

and np(1-p) >= 10 => 500* 0.032 * (1- 0.032) = 15.488 >=10

c. Null Hypothesis : H0: p <= p0proportion of children who eat recommended number of servings is as same as earlier

Alternative Hypothesis: Ha : p > p0proportion of children who eat recommended number of servings has increased from earlier

Test Statistics :

Z = ( p - po)/ sqrt(p0(1 - p0)/n) = ( 0.032 - 0.02)/ sqrt(0.02 * 0.98/500) = 0.012 / 0.00626 =1.9169

Zcriticialfor right tailed Z - test for alpha = 0.05 => Zcriticial = + 1.65

so here we can see that Z< Zcriticialso we can reject the null hypothesis and we can conclude that there is significant increase in proportion of children who eat recommended number of serving after advertisement campaign.

(d) P - value from Z - table for z = + 1.9169

p - Value = 0.0285

which is less than alpha = 0.05

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