Question

100 soldiers were randomly selected from the advanced raider unit in the name of the TARS .While this 100 TARS full bridle goes on the horse, the rate of hitting the target from 80 meters with arrow and bow is 92% and they can go on average 110 km per day on the horse.
The standard deviation of this distance is 16 km.
100 TARS can throw 50 arrow per minutes with 3.1 standard deviations.
However, previous research has shown that TARS can throw an average of 52 arrows with 4.3 standard deviations per minute.
An orientalist researcher claimed that this figure was an exaggeration and they could throw less than 52 arrows.
Another orientalist researcher claimed that the number of arrows throw by selected 97 Leh soldiers standard deviation was 6.2, and there was no difference between the standard deviations of the arrows throw by the TARS and Leh soldiers.

1.Test the assertion of the orientalist researcher with the p-value method at 1% significance level.

2.Test the assertion of the second orientalist researcher at the level of 0.01 significance.

Answer 1

1)

Ho :   µ =   52  
Ha :   µ <   52   (Left tail test)
          
Level of Significance ,    α =    0.010  
population std dev ,    σ =    4.3000  
Sample Size ,   n =    100  
Sample Mean,    x̅ =   50.0000  
          
'   '   '  
          
Standard Error , SE = σ/√n =   4.3/√100=   0.4300  
Z-test statistic= (x̅ - µ )/SE =    (50-52)/0.43=   -4.651  
          
critical z value, z* =       -2.3263   [Excel formula =NORMSINV(α/no. of tails) ]
          
p-Value   =   0.0000   [ Excel formula =NORMSDIST(z) ]
Decision:   p-value≤α, Reject null hypothesis       
Conclusion: There is enough evidence to support the claim of orientalist researcher