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Calculating mean, critical t-value, sample size

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1. A local bank needed information concerning the checking account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed.

2. Find the critical t-value that corresponds to c=0.90 and n=15.

3. A survey of 100 fatal accidents showed that 35 were alcohol related. Find a point estimate for p, the population proportion of accidents that were alcohol related.

4. The grade point averages of 10 randomly selected students are listed below. Construct a 90% confidence interval for the population standard deviation. Assume the data are normally distributed.
2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

5. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 2% with 95% reliability, how many students would need to be sampled?

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Solution Summary

This solution calculates several statistics values including mean, critical t-value and sample size

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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