Question

In the Star Wars franchise, Yoda stands at only 66cm tall. Suppose you want to see weather or not hobbits from Lord of the Rings are taller than Yoda, on average. Distributions are normally distributed. A sample of 7 hobbits, average height x=80cm and a standard deviation s=10.8 cm. Does sample evidence suggest at the 1% level of significance that the average hobbit is taller than Yoda? Sketch rejection and non-rejection

Answer 1

Given that the Yoda stands at only = 66cm tall. A sample of N = 7 hobbits, average height =80cm, and a standard deviation s=10.8 cm.

Also given that the distribution is normal but since the population standard deviation is not given hence T-distribution is applicable.

Since we want to see whether or not hobbits from Lord of the Rings are taller than Yoda, on average, the hypotheses are:

Based on the hypothesis it will be a right-tailed test.

Rejection region:

With the help of a given significance level, degree of freedom df = n-1=7-1=6 and the type of test, the critical region is calculated using excel formula for T-distribution which is =T.INV(0.99,6), thus tc = 3.143

So, reject Ho if t is greater than 3.143.

the Shaded region is not visible clearly since it is beyond the value 3.

Test Statistic:

P-value:

The P-value is computed using the T calculated above and the df using the excel formula for T-distribution which =T.DIST.RT(3.43,6), thus P-value = 0.0070.

Conclusion:

Since the p-value is less than 0.01 and t >3.707 hence we fail to reject the null hypothesis and conclude that there is sufficient evidence to support the claim,