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 p-value approach to conduct the following tests at = 0.10. H0: 15.4 against HA: > 15.4

a-1. Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your answer to 2 decimal places.) Test statistic

a-2. Approximate the p-value. 0.010 < p-value < 0.020 0.050 < p-value < 0.100 0.100 < p-value < 0.200

a-3. What is the conclusion?

Do not reject H0 since the p-value is greater than .

Do not reject H0 since the p-value is less than .

Reject H0 since the p-value is greater than .

Reject H0 since the p-value is less than . H0: = 15.4 against HA: 15.4

b-1. Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your answer to 2 decimal places.) Test statistic

b-2. Approximate the p-value. 0.050 < p-value < 0.100 0.200 < p-value < 0.400 0.100 < p-value < 0.200

b-3. What is the conclusion?

Reject H0 since the p-value is less than .

Reject H0 since the p-value is greater than . Do not reject H0 since the p-value is less than .

Do not reject H0 since the p-value is greater than .

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 =1.139
| to | =1.139
Critical Value
The Value of |t | with n-1 = 12 d.f is 1.356
We got |to| =1.139 & | 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 =1.1386
0.100 < p-value < 0.200
Do not reject H0 since the p-value is greater than