The following n = 10 observations are a sample from a normal population. 7.4 7.0 6.5 7.4 7.6 6.2 6.9 7.6 6.5 6.9 (a) find the mean and standard deviation of these data. (round your standard deviation to four decimal places.) mean standard deviation (b) test h0: μ = 7.5 versus ha: μ < 7.5. use α = 0.01. test statistic: t =

Mean, x:7

standard deviation(s)=0.4944

t=-3.1980

Step-by-step explanation:

given data

7.4 7.0 6.5 7.4 7.6 6.2 6.9 7.6 6.5 6.9

Count, N:10

Sum, Σx:70

Mean, x:7

Variance, s2:  0.24444444444444

Steps  

s2 =

     =

     =  

     =0.24444444444444

s =  

⇒s= 0.49441323247304

⇒s=0.4944

b) H0: μ = 7.5 versus Ha: μ < 7.5.

   α = 0.01.

    t=

    t=

    t=-3.1980

for 9 df and α = 0.01

t stat from table is -2.82

as t test is less than t

we reject the null hypothesis

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this