The following data on annual rates of return were collected from eleven randomly

Question

The following data on annual rates of return were collected from eleven randomly selected stocks listed on the New York Stock Exchange (“the big board”) and twelve randomly selected stocks listed on NASDAQ. Assume the population standard deviations are the same. At the 0.10 significance level, can we conclude that the annual rates of return are higher on the big board?

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State the decision rule for 0.10 significance level: H0: NYSE NASDAQ  and  H1: NYSE > NASDAQ.(Round your answer to 3 decimal places.)

Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)

Compute the test statistic. (Round your answer to 2 decimal places.)

State your decision about the null hypothesis.

Do not reject H0

Reject H0

NYSE NASDAQ 15.0 8.8 10.7 6.0 20.2 14.4 18.6 19.1 19.1 17.6 8.7 17.8 17.8 15.9 13.8 17.9 22.7 21.6 14.0 6.0 26.1 11.9 23.4

Explanation / Answer

Below are the null and alternate hypothesis

H0: NYSE    NASDAQ  and  H1: NYSE > NASDAQ

Decision rule: If p-value computed is less than significance level of 0.1, we reject the null hypothesis OR

If the value of computed test statistics is greater than critical value of test statistics (i.e 1.3232), we reject the null hypothesis.

From the given data we have

degrees of freedom = n1 + n2 - 2 = 21

The pooled estimate of the population variance

As value of test statistics t is less than the critcal value of test statistics 1.3232, we fail to reject the null hypothesis.

n1 11 n2 12 mu 1 16.9727 mu2 15.0333 sigma1 (s1) 5.1474 sigma2 (s2) 5.7615 Alpha 0.1 Critical t-value 1.3232 degrees of freedom 21

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