Question

ulture (USDA) uses sample surveys to produce important economic estimates. One pilot study estimated wheat prices in July and in September using independent samples of wheat producers in the two months. Here are the summary statistics, in dollars per bushel:

Month	Sample size	Sample mean	Sample SD
September	61	$3.21	$0.40
July	80	$3.11	$0.20

The September prices are higher on the average. But we have data from only a sample of producers each month. Can we conclude that the mean wheat prices were higher in September than they were in July? Or are these differences merely what we would expect to see due to random variation?

Let X = wheat prices in September and Y = wheat prices in July.

µx = the true population mean wheat prices in September, and µy = the true population mean wheat prices in July. Want to test the following

H0: µx = µy vs. Ha: µx > µy.

Find the observed t-value and P-Value of the test.

1. the observed t-value = 1.79 and 2.5% < P-Value < 5%.

2. the observed t-value = 1.79 and 5% < P-Value < 10%.

3. the observed t-value = 2.05 and 2% < P-Value < 2.5%.

4. the observed t-value = 2.05 and 2.5% < P-Value < 5%.

5. observed t-value = 2.12 and 1% < P-Value < 2%.

6. the observed t-value = 2.12 and 2% < P-Value < 2.5%.

7. the observed t-value = 2.23 and 1% < P-Value < 2%.

8. the observed t-value = 2.23 and 2% < P-Value < 2.5%.

9. the observed t-value = 2.51 and 0.5% < P-Value < 1%.

10. the observed t-value = 2.51 and 2% < P-Value < 2.5%.

Answer 1

Ans.

Hypothesis:

Note:- We find t test using MINITAB:-

Steps:-

1. Go to Stat -> Basic Statistics -> 2-sample t test
2. Enter data () in Summarized Data
3. Click Options and Select Alternative greater than
4. Click OK.

T- value = 1.79

P-value = 0.039 = 3.9%

=> 2.5 % < P-value = 3.9% < 5%

The observed t-value = 1.79 and 2.5% < P-value < 5%