Begnning in 1988 through 2013, the yearly numbers of publications in referred jo

Question

Begnning in 1988 through 2013, the yearly numbers of publications in referred journals by Professors Swartz are as follows: 2,0,0,1,5,1,2,4,2,3,4,2,3,3,2,2,4,2,2,5,1,3,2,6,1,3. In a test of whether his publication rate is 3 papers per year, the p-value = 2P(X<= 2.5) = 2 P( t26 <= (2.5-3)/(1.5033/ sqrt (26) ) = 2P ( t25 <= -1.696) = 0.102 is obtained and the null hypothesis is not rejected . There are various probelms with the assumptions underlying the test procedure. Describe some of the problems.

Explanation / Answer

Sol:

H0:mu=3

H1:mu not =3

alpha=0.05

Rcode to get t statistic and p value is:

no_of_publications <- c(2,0,0,1,5,1,2,4,2,3,4,2,3,3,2,2,4,2,2,5,1,3,2,6,1,3)
t.test(no_of_publications,mu=3)

Result:

One Sample t-test

data: no_of_publications
t = -1.6959, df = 25, p-value = 0.1023
alternative hypothesis: true mean is not equal to 3
95 percent confidence interval:
1.892792 3.107208
sample estimates:
mean of x
2.5

t=-1.6959

p=0.1023

p>0.05

do not reject H0

Accept Null hypothesis.

various probelms with the assumptions underlying the test procedure:

NORMALITY ASSUMPTION:

If the distribution of sample data of yearly number of publicatons is normal ,fine to use a t test.

But if the underlying distribution is not normal and sample size is small(rule of thumb n>30 per group if not too skewed;n>100 if the distribution is really skewed,the central imit theorem takes some time to kick in.cannot use t test

t test is very robust against the normality assumption.

if its not normal use wilcoxson rank sum test

INDEPENDENCE (CRITICAL)

For single mean as in this case,the observations within a sample must be indpendent.

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