The null and alternate hypotheses are Ho : 1 = 2 A random sample of 11 observati
ID: 3196459 • Letter: T
Question
The null and alternate hypotheses are Ho : 1 = 2 A random sample of 11 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4.6. A random sample of 8 observations from another population revealed a sample mean of 28 and a sample standard deviation of 3.6 At the 0.05 significance level, is there a difference between the population means? a. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.) The decision rule is to reject Ho if t b. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) Pooled estimate of the population variance c. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Test statistic d. State your decision about the null hypothesis (Click to select) Ho (Click to select) e. Do not reject k to select) RejectExplanation / Answer
a)
The decision rule is to reject H0 if t < -2.1098 or t > 2.1098
b)
Pooled estimate of population variance
Sp = sqrt[(n1 - 1)S1^2 + (n2 - 1)*S2^2/ n1 + n2 - 2]
Sp = sqrt [(11 - 1) *4.6^2 + ( 8 -1) * 3.6^2/(11+8 - 2]
= 4.394
c)
Test statistic = (X1 - X2) / Sp * sqrt(1/n1 + 1/n2)
= (23 - 28) / 4.394 * sqrt ( 1/11 + 1/8)
= -2.449
d)
Reject Ho because t < -2.1098
e)
The p value is between 0.01 and 0.02