Question

1. Ho is the national 10th grade students' reading comprehension score did not improve from 2011-2012; Ha is the national 10th grade students' reading comprehension score improved from 2011-2012. We reject the null hypothesis, stating the 10th grade students improved from 2011-2012, but in reality, they did not make any improvement. What type of statistical error we've made? In which way we can reduce the chance to make such error (2 points)? A. Type I error. Increase the sample size. B. Type II error. Increase the sample size. C. Type I error. Reduce the sample size. D. Type II error. Reduce the sample size.

Answer 1

Type I error is rejecting the null hypothesis when it is true.
Type I error is also known as the level of significance, alpha
Alpha = P(type I error) = P(reject Ho | Ho)

In this case,
The null hypothesis, ho: the national 10th-grade students reading comprehension score didn't improve from 2011-2012.
An alternative hypothesis, h1: the national 10th-grade students reading comprehension score improve from 2011-2012.
The decision is to reject the null hypothesis when in fact the null hypothesis is true. Hence a type I error is conducted here.

Type I error can be reduced by:
1. reducing the level of significance
2. decreasing the sample size.

hence the correct statement is:

C. type I error, reduce the sampe size.