Find the critical value t* for a 95 % confidence interval. Use SurfStat or Stata

Question

Find the critical value t* for a 95 % confidence interval.

     Use SurfStat or Stata’s invttail function to get the correct degrees of freedom.

DATA:

factory   haiti   loss
44   40   4
50   37   13
48   39   9
44   35   9
42   35   7
47   41   6
49   37   12
50   37   13
39   34   5
45   38   7
32   40   -8
47   35   12
40   38   2
38   34   4
41   35   6
43   37   6
40   34   6
37   40   -3
39   43   -4
52   38   14
45   38   7
37   38   -1
38   41   -3
44   40   4
43   35   8
39   38   1
44   36   8

More info:

These data come from earlier editions of Introduction to the Practice of Statistics, by David Moore and George McCabe. Studies conducted for the US Agency for International Development (USAID). Wheat-soy blend (WSB) is prepared for emergency food relief. Vitamin C is added to the WSB when it is prepared in the US and shipped overseas for ready availability for disaster relief. There is a concern that vitamin C is lost in shipment and storage.

The researchers selected a simple random sample of 27 bags of freshly-prepared wheat-soy blend at the US preparation site, before shipment to Haiti. They took samples of the WSB, and assessed the Vitamin C content. The bags were specially marked so that they could be resampled 5 months later in Haiti.

The data consist of 27 pairs of measurements. The key variable for analysis is the difference between the factory measurement and the Haiti measurement. We'll create the difference in Stata as the first step in our data analysis. Theoretically, the value of Vitamin C in the Haiti sample can't be any larger than the US value. But because the vitamin C isn't completely uniformly mixed in, and there's some measurement error, so some of the differences might be negative.

The units on the vitamin C measurements are milligrams of vitamin C per 100 grams of WSB.

Explanation / Answer

As there are 27 paired observations , so degree of freedom =n-1=27-1=26

As invttail(n,p) is such that p is a right tail area from a t distribution with n degrees of freedom, we will usep=0.025 to know criticall value as both side area then willbe 0.05 in total.

Using following stata command we get critical value=2.0555

. display invttail(26,0.025)
2.0555294

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