In order to conduct a hypothesis test of the population mean

In order to conduct a hypothesis test of the population mean, a random sample of 13 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 16.0 and 1.9, respectively. Use Table 2

Use the critical value approach to conduct the following tests at = 0.10.

H₀: = 15.4 against H_A: 15.4

b-1.

Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

b-2.

Calculate the critical value(s). (Round your answers to 3 decimal places.)

b-3.

What is the conclusion?

Solution

Set Up Hypothesis
Null, H0: U=15.4
Alternate, H1: U!=15.4
Test Statistic
Population Mean(U)=15.4
Sample X(Mean)=16
Standard Deviation(S.D)=1.9
Number (n)=13
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =16-15.4/(1.9/Sqrt(12))
to =1.14
| to | =1.14
Critical Value
The Value of |t | with n-1 = 12 d.f is 1.782
We got |to| =1.14 & | t | =1.782
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 1.14 ) = 0.2771
Hence Value of P0.1 < 0.2771,Here We Do not Reject Ho

ANS:
to =1.14
The Value of |t | with n-1 = 12 d.f is 1.782
Do not reject H0 since the value of the test statistics is smaller than the critical value.