Question

Show all steps as demonstrated in class. All proportions should be rounded to 4 decimal places and z-scores to 2 decimal places for consistency and accuracy. 1. According to a recent Gallup poll, 10% of Americans do not eat breakfast. You wonder if this figure is different among PCC students. a. State the null and alternative hypotheses, and define the parameter. b. Suppose we take a random sample of 450 PCC students. Do we meet the conditions for the distribution of sample proportions? Be sure to check all conditions. c. Define the null model i.e. the distribution of sample proportions). d. Suppose in our sample of 450 PCC students, 57 did not eat breakfast. What is the Z-score for this outcome? What does it indicate about the conclusion of the hypothesis test?

Answer 1

(c) U let p be the proportions of Anurican not eating breakfast so p=0.10 (a) Null hypothesis plo: p=0.10 Alternative hypothesis Mi: p = 0.10 parameter i p=0.10 (b) sample size is n=450 conditions are up 7,10 and upli-p17110 So, np = 450X0:10 = 457/10 (condition satisfied) np (1-P) = 450x 0.1080.90 = 40.57110 (condition sansfied) Null model means p=0.10 which determines that proportion of pce student mot having breakfast i 0.10 (d) is estimate of population proportion & G.E(!) = P (1-B) 10:196578 0.8733 k-e 1.70 is S.E(A) le) p-valve = Pliz!> 1.70) whore 2 VN101) - 0.08898 18) It u the probability of obtaining results as extreme as the observed results of a test, assuming that 10% of pic do not eat breakfast gr Tha= 5% and p value a and we do not reject to. x = 10% then p-value La and we reject Ho. Å = 57 = 0.1267 450 = 0.0157 . 450 Now zo Z-score. 0.1267-0.10 0.0157

For part g)

Since the level of significance (alpha) is not given. I am explaining with both 5% and 10%

If alpha = 5% = 0.05 then p value > alpha, then we do not reject Null hypothesis and conclude that proportion of PCC students not having breakfast is 10%

If alpha = 10% = 0.10 then p value < alpha, then we reject the null hypothesis and conclude that proportion of PCC students not having breakfast is not equal to 10%