A statistics instructor wishes to see whether a new software program reduces the

Question

A statistics instructor wishes to see whether a new software program reduces the number or errors her students make when analyzing data. The teacher records the number of errors for each student before using the new software and after using the new software. Assume that the population of differences in errors before and after, follow a normal distribution. The t test for related samples may be used to determine if there was a significant decrease in the mean number of errors due to the effect of the new software program. Suppose the mean decrease in errors over all the six students is 1.5 errors with a standard deviation of differences of 1.64 errors.

Explanation / Answer

here sample size n=6

therefore degree of freedom =n-1=5

for std error =std deviation/(n)1/2 =1.64/(6)1/2 =0.6695

therefore test stat t=(d/std error)=1.5/0.6695=2.2404

for above test stat t and 5 degree of freedom ; p value =0.0376

as p value is lower then 0.05 level of signficance we can reject null hypothesis at 0.05 level.

we have sufficient evidence at 0.05 level that there was a significant decrease in the mean number of errors due to the effect of the new software program

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