Question

1. Insurance: Every year, 11% of the wheat crop is destroyed by hail. An insurance company takes a sample of 16 claims. The sample mean is 10.5% of the crop; the population standard deviation is .05 for the crop, with a = .01. Will crop losses be less than the population mean based on this study?

   1. H0:                  ________

   2. H0: _________

   3. z-score __________

   4. P= _____________

   5. Reject or fail to reject___________

Answer 1

Solution :

= 0.11

=0.105

=0.05

n = 16

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    = 0.11

H_a : < 0.11

Test statistic = z

= ( - ) / / n

= (0.105 - 0.11-) / 0.05 / 16

= -0.4

Test statistic = z = -0.4

P(z < -0.4 ) =  0.3446

P-value =0.3446

= 0.10

P-value >

0.3446 > 0.10

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that