Question

_{An oceanographer has an old bathymetric map of an area and thinks that the depth it shows may be incorrect. She has modern equipment with her, and decides to conduct a test to see if the map’s value of 72.4 fathoms is correct. She conducts a random sample of depth at 35 locations in the area. Her sample mean was found to be 73.2 fathoms. Based on previous studies with this equipment, we can assume that σ = 2.1 fathoms. Based on a 0.05 level of significance, can we say that the map is correct/incorrect? Use Microsoft Excel so solve this question (Show all Excel formulas used)}

Answer 1

null hypothesis:Ho μ		=	72.4
Alternate Hypothesis:Ha μ		≠	72.4

for 0.05 level with two tail test , critical z=			1.960    # (use norminv(0.975)
Decision rule:reject Ho if absolute test stat|z|>1.96

population mean μ=	72.4
sample mean 'x̄=	73.200
sample size    n=	35.00
std deviation σ=	2.100
std error ='σx=σ/√n=2.1/√35=	0.3550

test stat z = '(x̄-μ)*√n/σ= (73.2-72.4)/0.355 =

2.25

p value        =

0.0244 # use 2*(1-normsdist(2.25))

since p value <0.05 , we reject null hypothesis and conclude that map is incorrect