In the HSB data set, compare the standardized reading scores to the standardized
ID: 2930555 • Letter: I
Question
In the HSB data set, compare the standardized reading scores to the standardized math scores, i.e., test the null hypothesis that there is no difference between students’ reading and math abilities. (use = .01). Specify the null and alternative hypotheses, and report the values of Y¯ d, sd, the standard error of the mean difference, the sample size n, the value of the test statistic, t, and the pvalue associated with this value of t. Clearly state your decision regarding the null hypothesis and your conclusion in the context of the problem. Write down the 95% confidence interval for µ1 µ2 and interpret this interval.
CONCPT Std. Dewiation Minimum Maximum 7053-2.6200 7082-2.6000 7055 Public 1.1900 1.1900 1.1900 -0047 506.0000 056794.0000 Total 2.6200 Independent Samples Test Levene's Test for Equality of f Mean 99% Confidence Interval of the Sig. (2Mean Sid Up Difference Difference Equal 14 024 876-.775 598 439 .061 079 266 Equal 14 variances not 773 129.619 441 .061 .079 269 Independent Samples Test Levene's Test for Equality of t-test for Equality of Means 95% Confidence Interval (2 MeanStd. Error df tailed) Difference DifferenceLower Equal variances 024.876.775 593439 061 .079 217 Equal variances .773 129.619 44 061 .079 219 .096 not assumedExplanation / Answer
HYpotheses: the null and alternative hypotheses are as follows:
H0:mu1-mu2=0 (there is no difference between population mean reading and population mean math scores)
H1:mu1-mu2=/= 0 (there is differenec between population mean reading and population mean math scores)
Since, no direction is specified, the test is two-tailed.
Look for indeoendent samples t test output. The Levene's test has a p value>0.05, which means variability of two groups are same. Thus, refer to output of first row. The t(598) is: -0.775, p value is: 0.439, standard error of difference is 0.079. The p value is not less than 0.01, therefore, fail to reject null hypothesis. There is insuffiicent sample evidence to conclude that there is significant differenec between population mean reading and population mean math scores. The 95% c.i for mu1-mu2=(-0.217, 0.094). Thus, one can be 95% confident that the interval captures the difference between true population mean reading and math scores.