A data set includes data from student evaluations of courses. The summary statistics are
n=83,
x=3.43,
s=0.55.
Use a
0.01
significance level to test the claim that the population of student course evaluations has a mean equal to
3.50.
Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Determine the test statistic.
(Round to two decimal places as needed.)
Determine the P-value.
Answer:
here null hypothesis i.e. Ho :the population of student course
evaluations has a mean equal to 3.50. and
alternative hypotheisi is H1:the population of student course evaluations has a mean not equal to 3.50.
Here, n=83, x(statistic)=3.43, s=0.55 , alpha=0.01 and parameter is 3.5
test statistics is t=( statistic- parameter) / standard error
standard error = s/√n =0.55/ square root (83)
=0.06037
now t= (3.43-3.5)/0.06037
t= -1.16
p value is t value at (0.01,(83-1))= 2.637
here |t| calulated value is 1.16 which is less than tabulated t value 2.637
Hence the null hypothesis is fail to reject. The population of student course evaluations has a mean equal to 3.50.
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