Provided below are summary statistics for independent simple random samples from

Question

Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. X bar_1 = 17, S_1 = 2, n_1 = 20, x bar_2 = 28, s_2 = 8, n_2 = 10 Left-tailed test, alpha = 0.05 90% confidence interval What are the hypotheses for the t-test? Find the test statistic. t = (Round to three decimal places as needed.) Find the critical value. -tg = (Round to three decimal places as needed.) What is the conclusion of the hypothesis test? Reject H_0. There is insufficient evidence that mu_1 is less than mu_2. Reject H_0. There is sufficient evidence that mu_1 is less than mu_2. Do not reject H_0. There is insufficient evidence that mu_1 is less than mu_2. Do not reject H_0. There is sufficient evidence that mu_1 is less than mu_2. The 90% confidence interval is from to. (Round to three decimal places as needed.)

Explanation / Answer

a) The test is left tailed, therefore, H0:mu1=mu2 (The difference in mean price is zero)

H1:mu1<mu2 (mean price of population 1 is less than population 2)

b) For independent groups,

SE(x1bar-x2bar)=sqrt [SE^2(x1bar)+SE^2(x2bar)]=sqrt [s1^2/n1+s2^2/n2]=sqrt [2^2/20+8^2/10]=2.57

The observed difference is x1bar-x2bar=17-28=-11

t=[(x1bar-x2bar)-0]SE(x1bar-x2bar)=(-11-0)/2.57=-4.28

c) For df=9, the critical value of t: 1.833.

d) The test statistic do not fall in critical region. Therefore, fail to reject H0. Option C)

e) ME=tcritical*SE(x1bar-x2bar)=1.383*2.57=3.554

90% c.i=(x1bar-x2bar)+-3.554=-11+-3.554=-14.554 to 7.446

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