Question

We have 5-year statistics of the average amount of wheat crop (tons) harvested from 1 km2 per year, the results are as follows: 560, 525, 496, 543, 499. The sample average and standard deviation are 524.6 and 27.6821 respectively. We want to test the hypothesis that whether the mean wheat crop is 550 tons per 1 km2 per year or not (alpha = 0.05). Answer the following questions.

What is the value of the test statistic? (round to 4 decimal places)

Identify the critical region by providing the positive critical value? (use 3 decimal places)

What is the 95% lower confidence limit? (round to 2 decimal places)

What is the 95% upper confidence limit? (round to 2 decimal places)

What is the conclusion of the test? (type your choice as either reject or fail to reject)

Answer 1

Step 1:

Ho: = 550

Ha: 550

Null hypothesis states that the mean wheat crop is 550 tons per 1 km2 per year

Alternative hypothesis states that the mean wheat crop is not equal to 550 tons per 1 km2 per year

Step 2: Test statistics

n = 5

sample mean = 524.6

sample sd = 27.6821

Assuming data is normally distributed and as population sd is not given, we will calculate t stat

t = - 2.0517

(1) t stat = - 2.0517

(2) t critical for two tailed test: +/- 2.776

As t stat does not fall in the rejection area, we fail to reject the Null hypothesis.

(3) 95% CI

t value = TINV( 0.05, 4) = 2.776

  

Lower limit = 490.23

Upper limit = 558.97

(4) As 550 falls in the range, we fail to reject the Null hypothesis.

Fail to reject