<prompt> Please answer with one of the option in the bracket. Write reasoning in between . Write answer in between .Q:A researcher is examining the relationship between socioeconomic status and IQ scores. The IQ scores of young American adults have historically been reported to be distributed normally with a mean of 100 and a standard deviation of 15. Initially, the researcher obtains a random sampling of 300 high school students from public schools nationwide and conducts IQ tests on all participants. Recently, the researcher received additional funding to enable an increase in sample size to 2,000 participants. Assuming that all other study conditions are held constant, which of the following is most likely to occur as a result of this additional funding?? A: Increase in range of the confidence interval, B: Decrease in standard deviation, C: Decrease in standard error of the mean, D: Increase in risk of systematic error, E: Increase in probability of type II error,  <response>: This is a question about sampling and statistical inference. The key points are:- The IQ scores are normally distributed with mean 100 and standard deviation 15. This distribution will not change with sample size.- The sample size is increased from 300 to 2000. - Larger sample sizes lead to more precise estimates of the population mean.- The standard error of the mean decreases as sample size increases. The standard deviation of the sample does not change with sample size.- Confidence intervals depend on the standard error. A smaller standard error leads to a narrower confidence interval.- Type II error relates to statistical power. With a larger sample size, statistical power increases, so the probability of type II error decreases.C: Decrease in standard error of the mean 