Question

Using α-005, is there sufficient evidence to conclude that less than 88% GMU students who utilize the food delivery robots skip breakfast? Conduct a full hypothesis test by following the steps below. p 0.8384 i. Define the population parameter in one sentence. Iternative hypotheses using correct notation. ii. State the significance level for this problem. iv. Check the three conditions of the Central Limit Theorem that allow you to use the one-proportion z-test using one complete sentence for each condition. Show work for the numerical calculation. Assume the population is large. v. Calculate the test statistic "by-hand." Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round while doing the calculation. Then, round the test statistic to two decimal places after you complete the calculation. Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this). vi. vii. viii. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.

Answer 1

i)
population parameter is all the GMU students who utilize the food delivery robots skip breakfast

ii)

Ho :   p =    0.88
H1 :   p <   0.88

iii)

Level of Significance,   α =    0.05

iv)

conditions

a)

sample size should be less than 5% of population,

here, population size is very large, so, sample size <0.05N

b) n p >5  

np=244 >5

c)nq>5

nq = 47>5

v)

Number of Items of Interest,   x =   244  
Sample Size,   n =    291  
          
Sample Proportion ,    p̂ = x/n =    0.8384  
          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0190  
          
Z Test Statistic =    Z = ( p̂-p)/SE =    -2.18

vi)

p-Value   =   0.015

vii)

p-value<α , reject null hypothesis           

viii)

since, we reject Ho, so, there is enough evidence to conclude that less than 88% of  GMU students who utilize the food delivery robots skip breakfast at α=0.05