3 Walleye Trouble Walleye is a fish that is native to the no

3. Walleye Trouble. Walleye is a fish that is native to the northern United States and Canada that is known for its excellent taste. It is especially popular in Minnesota where it is deemed their state fish. As a result it is often overfished in Minnesota lakes, especially Lake Mille Lacs. One way to measure the health of the population is through the average length of the fish because fish grow their entire lives. The DNR considers the walleye population in a lake to be strong if the mean length of walleye in the lake is more than 17 inches. The DNR conducted a fish survey and netted 660 walleye and calculated an average length of 17.5 inches and a standard deviation of 4.68 inches. Is this sufficient evidence to say the walleye population in Lake Mille Lacs is strong? (a) Conduct a hypothesis test of the above situation, using a significance level of =0.05. i. Identify the hypotheses H0 and HA. • µ = 17 • µ = 17.5 • x = 17.5 • x > 17.5 • µ > 17.5 • µ > 17 ii. Find the test statistic. iii. Using the table below, select the appropriate value for the p-value based on your alternative hypothesis. P(T < t) 0.991 P(T > t) 0.009 P(T > |t|) 0.018 iv. (FREE RESPONSE) Provide an interpretation of the p-value you chose from the above table within the context of the problem. v. Make a decision about H0. • Reject the null hypothesis. The p-value p < = 0.05. • Reject the null hypothesis. The p-value p > = 0.05. • Fail to reject the null hypothesis. The p-value p < = 0.05. • Fail to reject the null hypothesis. The p-value p > = 0.05

Solution

i)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   17  
Ha:    u   >   17  

ii)
              
As we can see, this is a    right   tailed test.      
Getting the test statistic, as              
              
X = sample mean =    17.5          
uo = hypothesized mean =    17          
n = sample size =    660          
s = standard deviation =    4.68          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.744707816   [ANSWER, TEST STATISTIC]

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iii)

Also, the p value is              
              
p =    0.00302824          

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iv)
              
As P < alpha = 0.05, we   REJECT THE NULL HYPOTHESIS.      

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