Question

In: Statistics and Probability

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

Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 67 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = cm s = cm

(ii) Assume the slab thickness has an approximately normal distribution. Use a 5% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

(a) What is the level of significance?

Solutions

Expert Solution

Given that,
population mean(u)=67
sample mean, x =61.8125
standard deviation, s =10.6472
number (n)=16
null, Ho: μ=67
alternate, H1: μ!=67
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.131
since our test is two-tailed
reject Ho, if to < -2.131 OR if to > 2.131
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =61.8125-67/(10.6472/sqrt(16))
to =-1.9489
| to | =1.9489
critical value
the value of |t α| with n-1 = 15 d.f is 2.131
we got |to| =1.9489 & | t α | =2.131
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -1.9489 ) = 0.0703
hence value of p0.05 < 0.0703,here we do not reject Ho
ANSWERS
---------------
a.
level of significance =0.05
i.
sample mean, x =61.8125
standard deviation, s =10.6472
ii.
null, Ho: μ=67
alternate, H1: μ!=67
test statistic: -1.9489
critical value: -2.131 , 2.131
decision: do not reject Ho
p-value: 0.0703
we do not have enough evidence to support the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

orchestra answered 1 year ago
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