5. If the error for estimating µu was within 4 units, how many should we sample at 98% Confidence level to accomplish that if s = 29?

The scores for a certain standardized test have a population mean of μ=285 with a population standard deviation σ=125.  You take an SRS of size 400 find that the sample mean \bar x is 288. The margin of error in a 90% confidence interval for μ based on this sample is

Please solve by using R calculator or excel. Show all work.

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming s=10.7 based on earlier​ studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size​ required?

An automobile manufacturer wants to estimate the mean gasoline mileage that its customers will obtain with its new compact model. How many sample runs must be performed so that the estimate is accurate to within 0.5 mpg at 98% confidence? Assume that ? = 2

Please see below. I need help with this.

Sample Size: We have established that the body weights of 20-29 year old U.S. males are σ=40 pounds. How many observation do we need in order to estimate mean body weight µ with 95% confidence and a margin of error of ± 10 pounds?

A researcher wishes to estimate the true proportion of all speeders who exceed the posted speed limit on a particular stretch of road in the Canyonlands National Park where there are frequent accidents. How large should the sample be so that with 91 percent confidence, the sample proportion will not differ from the true proportion by more than 0.261?z = n ⩾

We want to estimate the average time it takes to get relief after taking a painkiller by all patients. Suppose that the population is normally distributed with a standard deviation of 23 minutes. How large a sample should be taken to estimate the population mean time to within 3 minutes with 99% confidence? Sample Size =