Question

Research at the University of Toledo indicates that 50% of students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Test at the .05 level of significance.

a What is the Null Hypothesis?

Ho µ _____ _____

Ha µ _____ _____

b Hypothesis test being performed is? (Circle answer) Left tail test, Right tail test Two tail test

c Degrees of freedom, df for the test statistic t is?

df = ________

d Numerical value of the test statistic t is? (Show work)

t = ________ e Method of calculation (Circle answer) Table, Computer algorithm

Pvalue = _______

f Your Decision is? (Circle answer) Null Hypothesis, Alternate Hypothesis, Insufficient information to make decision

Answer 1

H0 $\mu =0$

H1 $\mu \neq 0$

b)

It is a two tail test as we are checking for equal or not equal and not greater than or less than

c) Degrees of fredom for t statistics can be calculated by taking sample size and subtract 1=df=100-1=99

d) $t= (\bar{x}-\mu )/(s/\sqrt{n})$

mu=0.5

$\bar{x}=48/100=0.48$

s=0.5 as it is equal to mu=0.5

n=100

t=(0.48-0.5)/(0.5/10)= - 0.4

e) p=1.984 df=99 but in table we have df=100 and alpha=0.025using tables

f) Decision is if p<alpha reject H0

since p=1,984>0.025 hence we accept Null Hypothesis