Question

7. A biologist was interested in determining whether sunflower seedlings treated with an extract from Vincaminor roots resulted in a lower mean height of sunflower seedlings than the standard height of 15.7 cm. The biologist treated a random sample of n = 33 seedlings with the extract and subsequently obtained the a sample mean of 15.664 cm and a sample standard deviation of 2.544 cm. Test the claim that the mean height is less than 15.7 cm. 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

olution :

Given that,

Population mean = = 15.7

Sample mean = = 15.664

Sample standard deviation = s = 2.544

Sample size = n = 33

Level of significance = = 0.05

This is a left tailed test.

The null and alternative hypothesis is,

Ho: 15.7

Ha: < 15.7

The test statistics,

t = ( - )/ (s/)

= ( 15.664 - 15.7 ) / ( 2.544 /33)

= -0.081

p-value = 0.4679

The p-value is p =0.4679 > 0.05 it is concluded that the null hypothesis is fails to rejected.

Conclusion :

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

population mean μ is less than 15.7, at the 0.05 significance level.