Answer:
t = -1.633<2.06
<u>Step 1</u>
Here χ is the sample mean
μ is the population mean
S is the sample standard deviation
n be the sample size
The degrees of freedom γ =n-1
<u>Step 2:-</u>
a) we will use t- distribution test
Here sample size n = 25
the sample mean χ =640
population mean μ =650
sample standard deviation S=30
<u>Step 3:</u>-
b) we will use two tailed test or left tailed test
Null Hypothesis H0 : μ=650
Alternative Hypothesis Ha:μ<650
<u>Step 4:</u>-
c)
[tex]t = -1.633
<u>Step 5</u> :-
<u>Degrees of freedom:-</u>
The d<u>egrees of freedom of t- distribution</u>
γ = n-1 = 25-1 = 24
The table value of t are 5% level with 24 degrees of freedom For two tailed test is 2.06
<u>Step 6:</u>-
Since the calculated value of t < tabulated value of t, so we accepted the null hypothesis.
The data support the assumption of a population is normally distributed