In the HSB data set, compare the standardized reading scores to the standardized
ID: 2930557 • 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.
95% Confidence Interval of Std. Std. Error he Difference Sig. (2- MRan Deviatinn air1Explanation / Answer
The hypotheses are as follows:
H0:mud=0 (there is no difference bteween standardized reading scores and standardized math scores)
H1:mud=/=0 (there is difference between standardized reading and standardized math scores)
where, d=reading score-math score
From output, dbar=0.053, sd=7.841, SEdbar=0.320. The output futher shows that t(599)=0.165, p=0.869. Sample size, n=df+1=599+1=600. The p value is not less than alpha=0.05, therefore, fail to reject null hypothesis. There is insufficient sample evidence to conclude that there exists significant difference between standardized reading and standardized math scores. The 95% c.i for mud=(-0.576, 0.682). One can be 95% confident that the interval captures the true population mean difference between standardized reading and standardized math scores.