Question

Homework Problem 5 Salt-free diets are often prescribed to people with high blood pressure. Participants were randomly selected for the study and the following data were obtained as part of a study to measure the effect on diastolic blood pressure as a result of following a salt-free diet for two weeks. Assume the differences in diastolic readings are normally distributed in the population. Did completing the salt-free diet result in a significantly different diastolic blood pressure of participants? Use a t-critical of 2.365. Before 95 110 106 88 93 103 95 88 After 92 105 102 89 92 101 96 88 a. What are the null and the alternative hypotheses? (1 pt) b. Are the assumptions necessary for inference met? (1 pt) c. Perform the appropriate test including the formula that you used, and report the calculated value of the t-statistic. (6 pts) d. State your conclusion. (2 pts)

Answer 1

a)Null and Alternative hypothesis:

H₀ : The Salt-free diets is not effective for high blood pressure peoples

H₀ : $\mu$ _d =0

Against

H₁ : The Salt-free diets is effective for high blood pressure peoples.

H₀ : $\mu$ _d $\neq$ 0

$\mu$_d =  $\mu$y- $\mu$ x

d _i = y_{​​​​​​I} - x_{​​​​​​i}

b) Assumption required to use paired t-test

1) sample size (n <30) small sample.Therefore small sample size t test is appropriate

2)The difference in distolic readings are normally distributed in the population

3)The data were obtained of participants before the salt-free diet and after the salt-free diets fir two weeks.

Test statistic:

P t = Ps 'n

Follow t Distribution with (n-1) degree of freedom.

Σ1 d; d

2 (Σ" d; n-1 nd 2 = Ps

n= number of paired observations

Observation table:

Before (xi)	After (yi)	d i	d i 2
95	92	-3	9
106	102	-4	16
88	89	1	1
93	92	-1	1
103	101	-2	4
95	96	1	1
88	88	0	0
110	105	-5	25
		=-13	=57

Σ1 d; d

$\bar{d}=\frac{-13}{8}$

$\bar{d}=$ -1.625

2 (Σ" d; n-1 nd 2 = Ps

$s_{d}=\sqrt{\frac{(57-8*(-1.625)^{2})}{8-1}}$

S _d = 2.2638

$t=\frac{-1.625}{2.2638/\sqrt{8}}$

t=-1.625/0.8004

t=-2.0302

Cal | t |=2.0302

Critical value t= 2.365

Cal |t |< critical value t

Therefore we failed to reject the null hypothesis

d) There is insufficient evidence to conclude that the salt-free diet is results in a significantly different distolic blood pressure of participants.