Question

A basis is a kind of fish that lives mostly in lakes of rivers I don't bus is a nearby lake name Silverlake have an average length of 12.3 inches with a standard deviation of 3 inches recently fisherman in Silverlake told a reporter that this year they have been catching adult bus that are smaller than usual a research group interested in the size of the fish took a random sample of 100 adults bus from Silver Lake that researchers found that the mainland of the bus in the simple was 11.2 inches which of the following is the most appropriate statistical conclusion

Answer 1

Solution :

Given that ,

= 12.3

= 11.2

= 3

n = 100

The null and alternative hypothesis is ,

H0 :   = 12.3

Ha : < 12.3

This is the left tailed test .

Test statistic = z

= ( - ) / / n

= ( 11.2 - 12.3 ) / 3 / 100

= -3.67

The test statistic = -3.67

P - value = P (Z < -3.67 ) = 0.0001

P-value = 0.0001

= 0.05

0.0001 < 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to test the claim .