Snow avalanches can be a real problem for travelers in the western United States

Question

Snow avalanches can be a real problem for travelers in the western United States and Canada. One of the types of avalanches is called the slab avalanche and has been studied extensively in Canada. These avalanches have an average snow thickness of 67cm. The ski patrol in Colorado is beginning their study on slab avalanches. A random sample of 16 avalanches yield an average of 61.8 cm with a standard deviation of 10.6cm. Use the 99% confidence level to figure out if the avalanches in Colorado are different than Canada.

Explanation / Answer

Given that,
population mean(u)=67
sample mean, x =61.8
standard deviation, s =10.6
number (n)=16
null, Ho: =67
alternate,avalanches in Colorado are different than Canada H1: !=67
level of significance, = 0.01
from standard normal table, two tailed t /2 =2.947
since our test is two-tailed
reject Ho, if to < -2.947 OR if to > 2.947
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =61.8-67/(10.6/sqrt(16))
to =-1.962
| to | =1.962
critical value
the value of |t | with n-1 = 15 d.f is 2.947
we got |to| =1.962 & | t | =2.947
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -1.9623 ) = 0.0686
hence value of p0.01 < 0.0686,here we do not reject Ho
ANSWERS
---------------
null, Ho: =67
alternate, H1: !=67
test statistic: -1.962
critical value: -2.947 , 2.947
decision: do not reject Ho
p-value: 0.0686
we don't have evidence that avalanches in Colorado are different than Canada

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