A POLL OF 1300 RANDOMLY SELECTED STUDENTS IN GRADES 6 THROUGH-8 WAS CONDUCTED AND FOUND THAT 54% ENJOY PLAYING SPORTS. WOULD CONFIDENCE IN THE RESULTS INCREASE IF THE SAMPLE SIZE WERE 3000 INSTEAD OF 1300? WHY OR WHY NOT?
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A sixth form class consists of 6 girls and 9 boys. Three students from the class are chosen at random. The number of boys chosen is denoted by the random variable X. Show that a)P(X=0)=120/2730 b)P(X=2)=1296/2730
To determine whether confidence in the results would increase if the sample size were increased from 1300 to 3000, we need to consider the concept of sample size and its impact on confidence.
In general, increasing the sample size tends to improve the confidence in the results of a survey or poll. This is because a larger sample size provides a more reliable representation of the population being studied, reducing the potential for sampling errors and increasing the precision of the estimates.
Statistically speaking, larger sample sizes tend to result in smaller margins of error, meaning the estimated percentage is likely to be closer to the true percentage of the population. This leads to greater confidence in the results.
In this case, if the sample size were increased from 1300 to 3000, it is reasonable to expect that confidence in the results would increase. However, without knowing the specific margin of error associated with the initial sample size of 1300, it is difficult to provide a precise comparison.
Nonetheless, a larger sample size generally leads to more reliable results, so increasing the sample size from 1300 to 3000 would likely improve confidence in the findings of the poll.