A random sample of n measurements was selected from a population with unknown mean μ and known standard deviation σ.calculate a 95% confidence interval for μ for the given situation.  n=100, x=58, σ=20

A sample obtained from a population with σ = 12 has a standard error of σx̅ = 2 points. How many scores are in the sample?

A sample of n=36 scores has a standard error of 3. What is the standard deviation of the population from which the sample is obtained?

To compare the dry braking distances from 30 to 0 miles per hour for two makes of​ automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10​, can the engineer support the claim that the mean braking distances are different for the two makes of​ automobiles? Assume the samples are random and​ independent, and the populations are normally distributed.   The critical​ value(s) is/are   Find the standardized test statistic z for μ1−μ2.

The mean test score for a simple random sample of n=100 students was =80. The population standard deviation of test scores is σ=15. Construct a 95% confidence interval for the population mean test score μ.

In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?

A population has a mean of 300 and a standard deviation of 40. Suppose a simple random sample of size 100 is selected and x¯ is used to estimate μ .What is the probability that the sample mean will be within +/- 5 of the population mean?

A normal population has a standard deviation of 10. A random sample of 100 is taken to test H0:μ = 50, H1:μ ≠50 at the 0.05 significance level. The sample mean is 52. The p-value is?