Question

A single leaf is taken from 11 different tobacco plants. Each leaf is divided in half, and given one of two preparations of mosaic virus. We wish to examine if there is a difference in the mean number of lesions from the two preparations.

Plant Prep1 Prep2

-----------------

1    18    14

2    20    15

3     9     6

  4    14    12

  5    38    32

  6    26    30

  7    15     9

  8    10     2

  9    25    18

10     7     3

11    13     6

a) Does the data suggest that the mean number of lesions in leaves subjected to preparation 1 is larger than 15 lesions? Use a = 0.05.

b) Explain what would a type II error represent in (a).

Solve the problem using SPSS.

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

test statistic= 4.353

P value=0.001

Since P value <0.05 therefore SIGNIFICANT.

Decision: REJECT NULL HYPOTHESIS H0.

Conclusion: We have sufficient evidence to conclude that there is a difference in the mean number of lesions from the two preparations.

a) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

t test= 0.992

P value= 0.345/2= 0.1725

Since P value> 0.05 therefore NOT significant.

Decision: Do not reject null hypothesis H0.

Conclusion:We do not have sufficient evidence to conclude that he mean number of lesions in leaves subjected to preparation 1 is larger than 15 lesions.

b) Type II error is here falsely rejecting alternative hypothesis when it is true. In this case we may be due to some error falsely rejecting alternative hypothesis that is the mean number of lesions in leaves subjected to preparation 1 is larger than 15 lesions.