Body weight for students in NMSU is Normally distributed In

Body weight for students in NMSU is Normally distributed. In a report, it stated that the average weight for NMSU students is about 160 pounds. A researcher read the report, and he suspect that the average weight is below 160 pounds. To justify, he collected a SRS of 25 students from NMSU and the sample mean is 156.3 pounds, with a standard deviation of 12 pounds. (1) (6pts)Suppose you know the population standard deviation of NMSU students is 10 pounds, perform an appropriate test to do the analysis on 0.05 significance level. (Choose between z test and t test).

(2) (6pts)Suppose you DON’T know the population standard deviation, perform an appropriate test to do the analysis at 0.05 significance level. (Choose between z test or t test). PLease help I don\'t understand!

Solution

WHEN POPULATION S.D IS KNOWN, WHICH IS 12
Test Used: Z-Test For Single Mean
Set Up Hypothesis
Null, average weight is equal 160 pounds H0: U=160
Alternate, average weight is below 160 pounds H1: U<160
Test Statistic
Population Mean(U)=160
Given That X(Mean)=156.3
Standard Deviation(S.D)=10
Number (n)=25
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=156.3-160/(10/Sqrt(25)
Zo =-1.85
| Zo | =1.85
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.85 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -1.85 ) = 0.0322
Hence Value of P0.05 > 0.0322, Here we Reject Ho

We cliam that average weight is below 160 pounds

WHEN POPULATION S.D IS UNKNOWN, WHICH IS 12 [ t-test ]
Set Up Hypothesis
Null, H0: U=160
Alternate, H1: U<160
Test Statistic
Population Mean(U)=160
Sample X(Mean)=156.3
Standard Deviation(S.D)=12
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =156.3-160/(12/Sqrt(24))
to =-1.542
| to | =1.542
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.711
We got |to| =1.542 & | t | =1.711
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -1.5417 ) = 0.06812
Hence Value of P0.05 < 0.06812,Here We Do not Reject Ho

We cliam that average weight is does n\'t below 160 pounds