Dean suspects that statistics teacher increase the grades of the class of 75 students due to his endless love to his beloved students. Dean realized that average grade of previous statistics classes is 64 and she took some of the exams from student affairs departments and note the following grades: 65 75 98 34 76 52 80 84 68. Please help dean to conduct a statistical analysis and interpret the results.

Ho: μ=64 

H1: μ>64

test statistic: 0.9996

critical value: 1.8595

decision: fail to reject Ho

p-value: 0.17338

Therefore, there is no evidence that the teacher increase the grades of the class of 75 students due to his endless love to his beloved students.

Step-by-step explanation

Given that,

population mean(u)=64

sample data: (65 , 75 , 98 , 34 , 76 , 52 , 80 , 84 , 68 )

sample mean, x =70.2222

standard deviation, s =18.6734

number (n)=9

null, Ho: μ=64 

alternate, H1: μ>64

level of significance, alpha = 0.05

from standard normal table, right tailed t alpha/2 =1.8595

since our test is right-tailed

reject Ho, if to > 1.8595

we use test statistic (t) = x-u/(s.d/sqrt(n))

to =70.2222-64/(18.6734/sqrt(9))

to =0.9996

| to | =0.9996

critical value

the value of |t alpha| with n-1 = 8 d.f is 1.8595

we got |to| =0.9996 & | t alpha | =1.8595

make decision

hence value of |to | < | t alpha | and here we fail to reject Ho

p-value :right tail - Ha : ( p > 0.9996 ) = 0.17338

hence value of p0.05 < 0.17338,here we fail to reject Ho