Question

An experiment was conducted to determine the effect of a high salt mean on the systolic blood pressure (SBP) of subjects. Blood pressure was determined in 12 subjects before and after ingestion of a test meal containing 10.0 gms of salt. The data obtained were:

Subject	SBP before meal	SBP after meal
1	120	147
2	130	140
3	139	148
4	120	115
5	123	122
6	140	157
7	131	144
8	123	134
9	125	140
10	130	165
11	131	133
12	142	153

1. Is a one-sided or two sided test needed here?
2. What is the mean SBP for each time period?
3. What is the standard deviation for each time period?
4. Which statistical test is appropriate to use on these data?
5. Carry out the hypothesis test(s) in question in above d. Use α=0.01
6. Are the means statistically different?
7. Find the 99% confidence interval for the difference of the two means on SBP. Interpret your finding                                                                                     

Answer 1

Here calculation are done with the help of R software.

(a). Here we can use one sided test also.

(b). Mean of SBP before meal =  129.5

Mean of SBP after meal = 141.5

(c). Standard deviation of SBP before meal = 7.6693

Standard deviation of SBP after meal = 14.2031

(d). Paired t test is appropriate to use on these data.

(e). Hypothesis:

H0: Mean of SBP before meal is equal to mean of SBP after meal.

H1: Mean of SBP before meal is not equal to the mean of SBP after meal.

Test statistic =  -3.7358 and critical value = -2.7181

P-value =  0.0032, here p-value is less than level of significance that's why we reject null hypothesis H0.

(f). Yes means are statistically significant.

(g). 99% confidence interval for the difference of two means on SBP = (-12.0412 ,-11.9588)

In the above interval we can see that zero is not included Thus mean difference of two meaans on SBP is not zero.

R code:

########### Paired t-test ######################################
# b = SBP before meal, a = SBP after meal
b = c(120, 130, 139, 120, 123, 140, 131, 123, 125, 130, 131, 142)
a = c(147, 140, 148, 115, 122, 157, 144, 134, 140, 165, 133, 153)
mean(b) ; mean(a)
sd(b); sd(a)
t.test(b,a , paired = TRUE,alternative = "two.sided", conf.level=0.01)
######## The End ################################################

Output:

> ########### Paired t-test ######################################
> # b = SBP before meal, a = SBP after meal
> b = c(120, 130, 139, 120, 123, 140, 131, 123, 125, 130, 131, 142)
> a = c(147, 140, 148, 115, 122, 157, 144, 134, 140, 165, 133, 153)
> mean(b) ; mean(a)
[1] 129.5
[1] 141.5
> sd(b); sd(a)
[1] 7.669301
[1] 14.20307
> t.test(b,a , paired = TRUE,alternative = "two.sided", conf.level=0.01)

Paired t-test

data: b and a
t = -3.7358, df = 11, p-value = 0.00329
alternative hypothesis: true difference in means is not equal to 0
1 percent confidence interval:
-12.04118 -11.95882
sample estimates:
mean of the differences
-12

> ######## The End ################################################
>