To conclude,

(a) The sample mean resonance frequency is 115.

(b) The confidence level of \(\displaystyle{I}_{{{1}}}\)\(=(114.4,115.6)\) is 90% and confidence level of \(\displaystyle{I}_{{{2}}}\)\(=(114.1,115.9)\) is 99%

asked 2021-05-08

asked 2021-08-10

(a) What is the value of c=1−α. Using the methods, construct a 1−α confidence interval for μ from the sample data. What is the value of μ given in the null hypothesis (i.e., what is k)? Is this value in the confidence interval? Do we reject or fail to reject H0 based on this information?

(b) using methods, find the P-value for the hypothesis test. Do we reject or fail to reject \(H_0\)? Compare your result to that of part (a).

asked 2021-05-19

asked 2021-06-08

When \(\displaystyle\sigma\) is unknown and the sample is of size \(\displaystyle{n}\geq{30}\), there are two methods for computing confidence intervals for \(\mu\). 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 \(\displaystyle\sigma\), 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 \(\displaystyle\sigma\). 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 \(\displaystyle\overline{{{x}}}={45.2}\) and sample standard deviation s=5.3. Compute 90%, 95%, and 99% confidence intervals for \(\displaystyle\mu\) using Method 2 with the standard normal distribution. Use s as an estimate for \(\displaystyle\sigma\). Round endpoints to two digits after the decimal.

asked 2021-05-09

asked 2021-05-26

You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 36 business days from February 24, 2016, through February 24, 2017, the mean closing price of Apple stock was $116.16. Assume the population standard deviation is $10.27.

asked 2021-05-07