It is appropriate to approximate hte binomial distribution by the normaldistribution, if np > 5 and ng = n(1—p) > 5, assuming that n is the size and p is the probability of success.

Question

asked 2021-05-14

When σ is unknown and the sample size is \(\displaystyle{n}\geq{30}\), there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When \(\displaystyle{n}\geq{30}\), use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

asked 2021-01-27

p (at least 11) = ?

asked 2021-05-25

Suppose that an i.i.d. sample of size 15 from a normal distribution gives X¯=10 and \(\displaystyle{s}^{{{2}}}\)=25. Find 90% confidence intervals for μ and \(\displaystyleσ^{{{2}}}\).

asked 2021-06-23

Let p be the population proportion for the situation. (a) Find point estimates of p and q, (b) construct 90% and 95% confidence intervals for p, and (c) interpret the results of part (b) and compare the widths of the confidence intervals. In a survey of 1035 U.S. adults, 745 say they want the U.S. to play a leading or major role in global affairs.