Question

Consider the following data on the output (tonnes/ha) of 10 randomly selected winter wheat farms in Co. Meath. 9.5 10.6 10.8 11.2 10.4 11.5 11.3 11.5 10.4 11.0 Given that: ( ) 3.476 2 10 1    i Xi X a. Compute the 95% confidence interval for the true mean output (tonnes/ha) of all winter wheat farms in Co. Meath . b. Using this 95% confidence interval, evaluate the claim that the mean output (tonnes/ha) of all winter wheat farms in Co. Meath is 11.3 tonnes/per ha . c. Using a t-test evaluate the claim that the mean output (tonnes/ha) of all winter wheat farms in Co. Meath is 11.3 tonnes/per ha . d. Compare and contrast your results for b and c above .

Answer 1

From the given data

n = total number of observations = 10

Let the output (tonnes/ha) of randomly selected winter wheat farms in Co. Meath be denoted by, X

Sample Mean is given as below:

... (I)

Sample Standard Deviation

... (II)

... (III)

a. The 95% confidence interval for the true mean output (tonnes/ha) of all winter wheat farms in Co. Meath is given below:

t(0.05,9) = t - tabulated value at 95% confidence for (10 - 1), i.e., 9 degrees of freedom = 2.262 ... (IV)

Hence the 95% confidence interval for the true mean output (tonnes/ha) of all winter wheat farms in Co. Meath is:

b. As the value 11.3 (given) is not within the 95% confidence interval computed from a, i.e., 11.3 > 11.0963 (Upper limit of 95% confidence interval), it is inferred that the mean output (tonnes/ha) of all winter wheat farms in Co. Meath is not 11.3 tonnes/per ha

c. The t-test statistic to evaluate the claim that the mean output (tonnes/ha) of all winter wheat farms in Co. Meath is 11.3 tonnes/per ha is given as per the below hypothesis

vs

The t-test statistic at 95% confidence is given below:

From (I), (II), and (III) the t-test statistic is calculated as below:

... (V)

From (IV) it is observed that the t-tabulated value from 95% confidence and 9 degrees freedom t(0.05,9) = 2.62

From (V) it is observed that the calculated t value is more than the t-tabulated value at 95% confidence and 9 degrees freedom i.e., 3.9303 > 2.62 we reject null hypothesis that the mean output (tonnes/ha) of all winter wheat farms in Co. Meath is 11.3 tonnes/per ha

d. Comparing the results from b and c, it is inferred that the claim mean output (tonnes/ha) of all winter wheat farms in Co. Meath is 11.3 tonnes/per ha (10 marks) is not correct.

Note: The above answer is from the known information in the given question. Whereas in the given question "Given that :( ) 3.476 2 10 1    i Xi X" is unclear if it can be corrected then the answer can be corrected appropriately.