Question

4. You always believed that the mean daily fish catch in June in Mörökölli resort was no more than 14 kg/day. A random sample was taken with the following results (in kg/day): 9, 13, 14, 21, 18, 14, 17, 10, 18, and 20. Was your belief you correct? Present and test the null and alternative hypotheses using the critical value approach. Use α = 0.03 as your significance level.

Answer 1

n= 10 ,s= 4.06 xbar= 15.4 kg/day, alpha=0.03 and $\mu= 14kg/day$

NULL HYPOTHESIS H0: $\mu < 14kg/day$

ALTERNATIVEHYPOTHESIS HA: $\mu > 14kg/day$

Under null hypothesis test statistic is

t= xbar-mu/S/sqrt(n)

t= 15.4-14/4.06/sqrt(10)

t=1.4/4.06/3.16

t=1.4/1.28

t=1.09

critical value of t with 10-1= 9 d.f at 0.03 level of significance for right tailed test is 2.15

CONCLUSION: SINCE CRITICAL VALUE OF t is GREATER THAN CALCULATED VALUE OF t .WE DO NOT REJECT NULL HYPOTHESIS AT 0.03 LEVEL OF SIGNIFICANCE FOR RIGHT TAILED TEST. HENCE MEAN DAILY FISH CATCH IS NO MORE THAN 14KG/DAY.