Proffessor Jennings claimes that only 35% of the students at Flora College work

Question

Proffessor Jennings claimes that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the the number of students with part-time or full-time jobs. A random sample of 79 students have jobs? Use a 5% level of significance.

a) What is the criteria needed to do the hypothesis test?

b) What assumption is needed if the criteria is all met, that allows us to do the hypothesis test?

c) State the null and alternate hypotheses

d) What is the level of significance

e) What is the value of the sample statistic

f) Find the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Is this a right-tail,left-tail,or two tailed test?

g) Based on you answers in parts a to f state your conclusion

h) Interpret your conclusion in the context of the application

I) Do the corresponding confidence interval How does it support your hypothesis test?

Explanation / Answer

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 79 students shows that 37 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.

Given that,
possibile chances (x)=37
sample size(n)=79
success rate ( p )= x/n = 0.4684
success probability,( po )=0.35
failure probability,( qo) = 0.65
null, Ho:p=0.35  
alternate, H1: p>0.35
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.46835-0.35/(sqrt(0.2275)/79)
zo =2.2055
| zo | =2.2055
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.206 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.2055 ) = 0.01371
hence value of p0.05 > 0.01371,here we reject Ho
ANSWERS
---------------
a. test weather the sample is large enough for test
b.
sample is approximately normally distributed
c.
null, Ho:p=0.35, alternate, H1: p>0.35
d. 0.05
e. test statistic: 2.2055
critical value: 1.64
decision: reject Ho
f. p-value: 0.01371

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