A random sample of 800 first-year students at a large university included 558 st

Question

A random sample of 800 first-year students at a large university included 558 students who had attended public high schools and 242 who had attended private schools. The average grade point average (GPA) was 3.52 for students horn public schools and 3.26 for students from private schools. Does the observed difference seem substantial? The author calculated the P value to be 0.10 and concluded that although "this study proved the null hypothesis to the true, ... the sample size is minuscule in comparison to the population." Did she prove the null hypothesis to be true? Are her results invalidated by the small sample size?

Explanation / Answer

Here p value =0.10

so if p value less than alpha value then we reject Ho

here we suppose alpha=0.05

pvalue=0.10 > 0.05

so we do not reject null hypothesis

She proved null hypothesis is true

And the small sample size result is invalideted becuase in you take small sample size your p value is decrease and you reject the null hypothesis

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