SPSS computation and Interpretation: The Asian economy faltered during the last few months of 1997

SPSS computation and Interpretation: The Asian economy faltered during the last few months of 1997. Investors anticipated that the downturn in the Asian economy would have a negative effect on the earnings of companies in the United States during the fourth quarter of 1997. The following sample data show the earnings per share for the fourth quarter of 1996 and the fourth quarter of 1997 (The Wall Street Journal, January 28, 1998).
 

a.  Formulate H₀ and H₁ such that rejection of H₀ leads to the conclusion that the mean earnings per share for the fourth quarter of 1997 are less than for the fourth quarter of 1996.

The null hypothesis is H₀: m _{earnings for 1997} ?³ m _{earnings for 1996.}?

OR is this correct?:  H₀: m_{earning in 1997} = m_{earnings in1996}

The alternative hypothesis is Ha: m _{earnings for 1997} <? m _{earnings for 1996}

Notice that this is a one-sided test because we’re testing if one mean is less than another, instead of if the two means are not equal to each other.  If the sample evidence suggests that the mean earnings for 1997 are greater than or equal to the mean earnings in 1996, do we reject the null hypothesis. ???

b. Use the data in the following table to conduct the hypothesis test. At alpha = 0.10, what is your conclusion?

We already decided that this would be a one-sided test.  Looking at the data, it will be a t-test (because we don’t know the population standard deviations) and it will be a matched-pairs test (paired-samples test), because each row of the data comes from one company – the two samples are NOT independent as they would be in a two-sample t-test. 

The results from SPSS are below:

The mean difference between the 1996 and 1997 earnings is 0.1243 with a 95% confidence interval of the difference of (-0.0642, 0.3128).  The two-sided p-value is p = 0.178, which gives us a one-sided p-value of p = 0.089.  This is low enough to reject the null hypothesis at the 0.10 level.  Therefore, we can reject the null hypothesis and assume that the earnings in 1997 were less than the earnings in 1996. 

As p-value is less than 0.10 (90% confidence), we reject the null hypothesis.  Thus, it can be interpreted that the mean earnings of firms has decreased significantly from Q4 1996 to Q4 1997.