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

a-1.

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

a-2.

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

a-3.

What is the conclusion?

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Side Note: In your explaination could you include which variable is which and why you know that, and also could you explain why you chose the Z tale for this problem. Thanks!

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 =1.1386
| to | =1.1386
Critical Value
The Value of |t | with n-1 = 12 d.f is 1.356
We got |to| =1.1386 & | t | =1.356
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 1.1386 ) = 0.13855
Hence Value of P0.1 < 0.13855,Here We Do not Reject Ho

ANS:
to =1.14
The Value of |t | with n-1 = 12 d.f is 1.356
Do not reject H0 since the value of the test statistics is smaller than the critical value