Question

1) A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Of the 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Test the student's claim at the 0.10 significance level.

a) The null and alternative hypothesis would be:

• H0:pF=pTH0:pF=pT
  H1:pF>pTH1:pF>pT
• H0:μF=μTH0:μF=μT
  H1:μF<μTH1:μF<μT
• H0:μF=μTH0:μF=μT
  H1:μF>μTH1:μF>μT
• H0:pF=pTH0:pF=pT
  H1:pF<pTH1:pF<pT
• H0:μF=μTH0:μF=μT
  H1:μF≠μTH1:μF≠μT
• H0:pF=pTH0:pF=pT
  H1:pF≠pTH1:pF≠pT

b) Determine the test statistic. Round to two decimals.

t=t=

c) Find the p-value and round to 4 decimals.

p =

d) Make a decision.

• Reject the null hypothesis
• Fail to reject the null hypothesis

e) Write the conclusion.

• There is not sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college.
• There is sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college.

2) You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.

Category	Observed Frequency	Expected Frequency
A	16
B	10
C	5
D	9
E	23

Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.

What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.)
χ2=χ2=

What are the degrees of freedom for this test?
d.f.=

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =


Is the p-value less than αα?

• yes
• no

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null
• accept the alternative

Answer 1