In the fall of 2000, 54% of the almost 34,000 first-year students attending one of the California State Universities had strong enough math skills to take an entry level course.

1)Based on a sample of 20 students, can we assume our calculations will be accurate?
My answer is: yes, I got .5398. Can someone double check me.

2) What value will we use for the standard deviation for a sample of 100 students:
My answer: 4.98

Any help would be appreciated.
Thanks

1) To determine whether our calculations will be accurate based on a sample of 20 students, we need to consider the concept of sample size and confidence level. The accuracy of our calculations depends on the size of the sample relative to the population and the desired level of confidence.

In statistical analysis, a larger sample size generally leads to more accurate results. However, there is no specific sample size that guarantees accuracy. To assess the appropriateness of our sample size, statistical tools like sample size calculators can be used. These calculators take into account factors such as the desired level of confidence, the margin of error, and the variability within the population.

If you have already performed a calculation and obtained a result of 0.5398, this could be interpreted as a point estimate or proportion estimate of the population parameter (percentage of first-year students with strong math skills). However, without the information regarding the margin of error and confidence level, we cannot determine the accuracy of this estimate.

In summary, to accurately determine whether our calculations are accurate based on a sample of 20 students, we need to consider the desired level of confidence, margin of error, and sample size. The use of statistical tools or guidelines can help make an informed decision.

2) To determine the value of the standard deviation for a sample of 100 students, we would need access to the individual math skill scores of these students. The standard deviation measures the dispersion or variability in a data set. Without the specific scores, it is not possible to determine the exact value of the standard deviation.

However, if you are looking for a rough estimate, you can use available statistics or assumptions. For instance, if you know or assume that the population standard deviation for math skills is 5, you could use this value as an approximation for the standard deviation of the sample. It is important to note that using the population standard deviation as a substitute for the sample standard deviation assumes that the sample is highly representative of the population and that there are no significant differences.

In conclusion, without the actual data or any reliable approximation, it is not possible to determine the value of the standard deviation for a sample of 100 students accurately.