Question

For each of the following write a hypothesis test by following the handout The Steps in Hypothesis Testing. This will be graded for participation only. Once you submit your work, you will be able to view the Feedback Key for this activity. You will have two similar problems to do next week be graded for accuracy. Ski Patrol: Avalanches: Snow avalanches can be real problems 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 engineering at the University of British Columbia. Slab avalanches studied in Canada have an average thickness of μ=67 cm. The Ski Patrol in Vail, Colorado is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thickness in cm. 59 51 76 38 65 54 79 62 68 55 64 67 63 74 65 79 A box-and-whiskers plot of the data shows no outliers and a normal probability plot shows a correlation statistic of 0.973. Check for normality and if applicable, use a 5% level of significance to test the claim that the meal slab thickness is Vail region is different from that in Canada.

Answer 1

There are no outliers and the median is almost equi-distant from lower and upper quartiles. So, the data is normally (or approximately normally) distributed.

Sample size is, n =16

n<30, small sample. So, we use t-score.

Sample mean, =63.6875

Sample standard deviation, s = =10.8795

Hypothesised population mean is =67 cm

Null Hypothesis(H0): μ =67 cm

Alternative Hypothesis(H1): μ 67 cm (two-tailed test).

(where, μ =Population mean slab thickness is Vail region).

Test statistic(t):

t =(​​​​​​)/(s/​​​​​​) =(63.6875 - 67)/(10.8795/​​​​​​) = -1.2179

Critical value:

For a two-tailed test, at 5% significance level, at n - 1 =15 degrees of freedom, the critical value of t is:

t_critical =2.1314

Decision criteria:

If absolute t > absolute t_critical, reject H0. Otherwise, do not reject H0.

Conclusion:

Since absolute t: 1.2179 < absolute t_critical, we failed to reject the null hypothesis(H0) at 5% significance level.

Thus, we do not have sufficient statistical evidence to claim that the population mean slab thickness in Vail region is different from that in Canada which is 67 cm.