Consider the following hypothesis statement using -0.10 and data from two vananc
ID: 3321513 • Letter: C
Question
Consider the following hypothesis statement using -0.10 and data from two vanances are equal and the populations and normally distibuted Complete parts a and b 2.5 n,+20 n2= 15 a. Calculate the appropriate test statistic and interpret the resut The test statistic is Round to two decimal places as needed) The critcal valuels) are) Round to two decimal places as nasded Use a comma to separate answers as meeded) Because the test statishc b. Identfy the p-alus from part a and imerpeet the resu Round to three Gemai places as needed ) interpret the revat. Choose the cornect ananer below A Sce the pwatue is less than the sondicance wvel do not secyte B. Sice the Pvalue is not less man sgnheance levet, de not reret the nil hypothesis C , Senen 1he p-value not less than the D. Since the pwaike is less than the sionfcance et thenl bypothess HP LE19OlwExplanation / Answer
Solution:
Part a
Here, we have to use two sample t test for the population means assuming equal population variances.
The test statistic formula is given as below:
t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]
Where Sp2 is pooled variance
Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)
From given data, we have
X1bar = 14.9
X2bar = 12
S1 = 2.5
S2 = 3.1
n1 = 20
n2 = 15
df = n1 + n2 – 2 = 20 + 15 – 2 = 33
= 0.10
Sp2 = [(20 – 1)*2.5^2 + (15 – 1)*3.1^2]/(20 + 15 – 2)
Sp2 = 7.6755
(X1bar – X2bar) = 14.9 – 12 = 2.9
t = 2.9 / sqrt(7.6755*((1/20)+(1/15)))
t = 2.9 / 0.9463
t = 3.0646
Test statistic = t = 3.06
Critical values = -1.69 and 1.69
Because the test statistic is greater than upper critical value, we reject the null hypothesis
Part b
P-value = 0.004
= 0.10
(By using t-table or excel)
Since p-value is less than the significance level, reject the null hypothesis
Correct answer: D.
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