Question

Using this data, Implement the following hypothesis test:

H₀: μ = 7.53

H₁: μ ≠ 7.53

DATA:

4.83
1.18
3.43
-0.36
4.01
7.35
14.63
8.86
6.25
6.47
8.84
5.8
2.6
10.44

A) Compute x

B) Compute S

C) Compute t₀

D) Find t_α/2,n-1 for a confidence levelof α = 0.05​

E) Based on t₀ andt_α/2,n-1, would you reject H₀?

F) What is the P-value for your t₀?

Answer 1

Solution:

a) For computing we have to first input all data in excel and use command ,

=AVERAGE( data_range )

Mean = = 6.02

B) For standard deviation use command in excel,

=STDEV( data_range )

S = 3.92

C)

The t-statistic is computed as follows:

−1.441

D) Based on the information provided, the significance level is α = 0.05, and the critical value for a two-tailed test is tc ​=2.16.

E) Since it is observed that |t| = 1.441 ≤ tc ​= 2.16, it is then concluded that the null hypothesis is not rejected

F) The p-value is p = 0.1732 ...........Using excel, =TDIST(1.44,13,2)

Done