Question

1. A sample of 100 randomly selected oranda goldfish has a mean length of 6.75 inches. Suppose it is known that the population standard deviation of lengths of orandas is 0.985 inches. Use a 0.05 significance level to test the claim that the mean length of an oranda is greater than 6.65 inches.

Fill in the following information as you test the above claim:

State the claim symbolically and the opposite of the claim.

H0:

h1:

Teststatistic:

P-value:

Conclusion:

Answer 1

Solution :

Given that,

Population mean = = 6.65

Sample mean = = 6.75

Population standard deviation = = 0.985

Sample size = n = 100

Level of significance = = 0.05

The null and alternative hypothesis is,

This a right (One) tailed test.

Ho: 6.65

Ha: 6.65

The test statistics,

z = ( - )/ (/)

= ( 6.75 - 6.65 ) / ( 0.985 /100)

= 1.02

p-value = P(Z > z )

= 1 - P(Z < 1.02)

= 1 - 0.8461

= 0.1539

The p-value is p =0.1539, and since p = 0.1539 > 0.05 , it is concluded that the null hypothesis is fails to reject.

Conclusion :

It is concluded that the null hypothesis Ho is fails to reject. Therefore, there is not enough evidence to claim that the

population mean μ is greater than 6.65, at the 0.05 significance level.