Question

Biostatistics with R

- Solve the following by evaluating the test statistic and p value. Suppose that the population mean of systolic blood pressure in the US is 115. We hypothesize mean systolic blood pressure is lower than 115 among people who consume a small amount (e.g., around 3.5 ounces) of dark chocolate every day. Assume that systolic blood pressure, X, in this population has a Normal distribution. To evaluate our hypothesis, we randomly selected 100 people, who include a small amount of dark chocolate in their daily diet, and measured their blood pressure. If the sample mean is x¯ = 111 and the sample variance is s = 32, can we reject the null hypothesis at 0.1 confidence level?

- Solve the following using the Confidence Interval Hypothesis Test approah and t.test() Approach. Use the Pima.tr data set to evaluate the hypothesis that the population mean of diastolic blood pressure for Pima Indian women is not 70.

library(MASS)

data("Pima.tr")

#str(Pima.tr)

?Pima.tr

Answer 1

here the level of significance would be 0.1 not the confidence level. (please check the question once again)

(first part) here we want to test the

null hypothesis H0:=115 and

alternate hypothesis Ha:<115

( this is left one-tailed test, since We hypothesize mean systolic blood pressure is lower than 115 among people who consume a small amount )

here we use t-test and t=|(-)|/(s/sqrt(n))=(111-115)/(32/sqrt(100))=|-1.25|=1.25 with n-1=100-1=99 df

one tailed critical t(0.1,99)=1.66 is more than calcuated t=1.25, so we fail to reject (or accept H0) and conclude that dark chocolate does not lower the systolic blood pressure.

(second part) here we want to test the

null hypothesis H0:=70 and

alternate hypothesis Ha:70(this is two tailed test)

from the given data we found

=71.26 ,s=11.48,n=200

now we can use t-test and

t=|(-)|/(s/sqrt(n))=(71.26-70)/(11.48/sqrt(200))=|1.55|=1.55 with n-1=200-1=199 df

the two tailed critical t(0.1,199)=1.65 is more than calculated t=1.55, so we fail to reject ( or accept )H0 and conclude that diastolic blood pressure for Pima Indian women is 70.