Question

3) A random sample of 100 pumpkins is obtained and the mean circumference is found to be 40.5 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean circumference of all pumpkins is equal to 39.9 cm.

Answer 1

Solution :

= 39.9

=40.5

=1.6

n = 100

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 39.9

Ha :     39.9

Test statistic = z

= ( - ) / / n

= (40.5-39.9 ) / 1.6 / 100

= 3.75

Test statistic = z = 3.75

P(z >3.75 ) = 1 - P(z < 3.75 ) = 1 - 0.9999

P-value =2 * 0.0001 =0.0002

= 0.05  

P-value <

0.0002 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that