Data file here: https://expirebox.com/download/e17be4959ea9f5fa963ad623e679f855.
ID: 3179071 • Letter: D
Question
Data file here: https://expirebox.com/download/e17be4959ea9f5fa963ad623e679f855.html
Use the Stata generate command to calculate the values for the Vitamin C loss. (or R, I suppose).
E. Find the test statistic and P value for the investigators’ alternative hypothesis in the output. Note: When Stata prints a P value as .000 or .0000, or SurfStat says the P value is 0, the P value is not literally 0, just very small!
F. Write a summary sentence for a disaster relief agency, answering this question: Using P < .05 as the criterion, is there evidence that vitamin C is being lost? In the Stata test command output, find the 95% confidence interval for the mean loss.
G. Using the point estimate and the confidence interval, write a sentence for a disaster relief agency answering this question: How much vitamin C is being lost, on average?
USEFUL 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.
The dataset is wsbhaiti.dta . The two measurements are the variables called factory and haiti. Create the differences
gen loss = factory - haiti
and get the summary statistics
summ loss, detail
(You'll see that there are some negative differences; look at the 4 smallest values of loss.) Since the sample size is only 27, we'll check the distribution assumptions carefully:
graph box loss qnorm loss
Use Stata to get a 95% confidence interval for the mean vitamin C loss:
ci mean loss
and then repeat these calculations from first principles.
Explanation / Answer
E. Find the test statistic and P value for the investigators’ alternative hypothesis in the output. Note: When Stata prints a P value as .000 or .0000, or SurfStat says the P value is 0, the P value is not literally 0, just very small!
Please see the R code as shown below
library(foreign)
data.df<- read.dta("C:\Users\586645\Downloads\Chegg\wsbhaiti.dta")
str(data.df)
summary(data.df)
# perform the t test
t.test(data.df$factory,data.df$haiti,paired = TRUE)
The t test result is
> t.test(data.df$factory,data.df$haiti,paired = TRUE)
Paired t-test
data: data.df$factory and data.df$haiti
t = 4.9589, df = 26, p-value = 3.745e-05 , the p value is very small close to zero - 0.00000374
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
3.122616 7.544050
sample estimates:
mean of the differences
5.333333
F. Write a summary sentence for a disaster relief agency, answering this question: Using P < .05 as the criterion, is there evidence that vitamin C is being lost? In the Stata test command output, find the 95% confidence interval for the mean loss.
As the p value is less than 0.05 and the difference in the mean is 5.33 , hence we can conclude that yes the vitamin C is being lost in the process
summary(data.df)
factory haiti
Min. :32.00 Min. :34.00
1st Qu.:39.00 1st Qu.:35.00
Median :43.00 Median :38.00
Mean :42.85 Mean :37.52
3rd Qu.:46.00 3rd Qu.:39.50
Max. :52.00 Max. :43.00
The 95% confidence interval of the t test is
95 percent confidence interval:
3.122616 7.544050
sample estimates:
mean of the differences
5.333333
G. Using the point estimate and the confidence interval, write a sentence for a disaster relief agency answering this question: How much vitamin C is being lost, on average?
Based on the analysis above , we see that the average vitamin C in factory is 42.85 and than in Haiti is 37.52. Hence we can conclude that on an average we are loosing 42.85-37.52 = 5.33 units of vitamin C in the process.
Also , based on the confidence interval values
95 percent confidence interval:
3.122616 7.544050
we can say that this difference can range from 3.122 to 7.544
Hope this helps
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