A study was done using a treatment group and a placebo group. The results are sh

Question

A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below Use a 0.10 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? A. H_0: mu_1 = mu_2 H_1: mu_1 > mu_2 B. H_0: mu_1

Explanation / Answer

a. H0 : 1 = 2

Ha : 1 2

Here population standard deviation are not equal that means

degree of freedom = [st2 /nt + sp2 /np] 2 / [(1/nt -1) (st2 /nt)2 + (1/np -1) (sp2 /np)2 ]

= [0.972 /28 + 0.562 /39]2 / [ (0.972 /28)2 (1/27) + (0.562 /39)2 (1/38)]

= 0.001734/ [ 4.182 * 10-5 + 1.7015 * 10-6 ]

= 39.84 = 40 in integer

t = (xplacebo - xtreatment) / sqrt [st 2 /n1 + sp 2 /n2 ]

t = (2.66 - 2.34)/ sqrt [0.972 /28 + 0.562 /39]

t = 0.32/ 0.204 = 1.568

P - value = 0.1247 [ from t - table]

COnclusion :

We failed to reject the null hypothesis . There is not sufficient evidence to warrant rejection of the claim that the two samples are from population with the same mean.

Confidence interval for sample mean difference 90% CI = (1 - 2 ) +- t40, 0.10 sqrt (st 2 /n1 + sp 2 /n2)

= (2.66 - 2.34) +- 1.6838 * sqrt [0.972 /28 + 0.562 /39]

= (-0.024, 0.664)

as the confidence interval consists zero that means samples are from same population.

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