Question

1. A randomized, double-blind, placebo-controlled study evaluated the effect of the herbal remedy Echinacea purpurea in treating upper respiratory tract infections in 2- to 11-year olds. Each time a child had an upper respiratory tract infection, treatment with either echinacea or a placebo was given for the duration of the illness. One of the outcomes studied was “severity of symptoms.” A severity scale based on four symptoms was monitored and recorded by the parents of subjects for each instance of upper respiratory infection. The peak severity of symptoms in the 337 cases treated with echinacea had a mean score of 6.0 (standard deviation 2.3). The peak severity of symptoms in the placebo group (n_p= 370) had a mean score of 6.1 (standard deviation 2.4). Test the mean difference for significance using an independent t-test. Discuss your findings.

Answer 1

Answer:

Given,

consider,

Null hypothesis Ho: mu1 = mu2

Alternate hypothesis  H1: mu1 != mu2

Test Statistic

X = 6 , s.d1 = 2.3 , n1 = 337

Y = 6.1, s.d2 = 2.4 , n2 =370

Now Test Statistic

Z = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)

substitute all known values

Zo = 6 - 6.1 / Sqrt(( 5.29 / 337) + (5.76 / 370))

Zo = - 0.57

Absolute | Zo | = 0.57

Now critical Value for 95% confidence interval is 1.96

i.e.,

|Z α| = 1.96

We got absolute |Zo | =0.566 &

| Z α | =1.96

Here we can give | Zo | < | Z α | and Here we don't reject the null hypothesis i.e.,Ho

P-Value = ( P != -0.57 )

p value = 0.5717

Hence the p value is less than than p0.05 < 0.5717,so we don't reject the null hypothesis

So that we conclude that we have evidence that there is no significance between treat with echinacea, symptoms in the placebo group