Answer:
We conclude that the average height of hobbit is taller than Yoda.
Step-by-step explanation:
We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.
From a sample of 7 hobbits, you find their mean height  = 80 cm with standard deviation s = 10.8 cm.
 = 80 cm with standard deviation s = 10.8 cm.
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<u><em>Let </em></u> <u><em> = average height of hobbit.</em></u>
<u><em> = average height of hobbit.</em></u>
So, Null Hypothesis,  :
 :  
  66 cm      {means that the average height of hobbit is shorter than or equal to Yoda}
 66 cm      {means that the average height of hobbit is shorter than or equal to Yoda}
Alternate Hypothesis,  :
 :  > 66 cm      {means that the average height of hobbit is taller than Yoda}
 > 66 cm      {means that the average height of hobbit is taller than Yoda}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about population standard deviation;
                      T.S. =   ~
  ~ 
where,  = sample mean height = 80 cm
 = sample mean height = 80 cm
              s = sample standard deviation = 10.8 cm
              n = sample of hobbits = 7
So, <u><em>test statistics</em></u>  =   ~
  ~ 
                               =  3.429
The value of t test statistics is 3.429.
<em>Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>
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Therefore, we conclude that the average height of hobbit is taller than Yoda.