The proprietor of a boutique in Wollongong wanted to determine the average age of his customers. A random sample of 25 customers revealed an average age of 32 years with a standard deviation of 8 years. Determine a 95% confidence interval estimate for the average age of all his customers.

A manager of a company believes that the average age of its customers is 40. However, theCEO of the company thinks that the average age of the company’s customers differs from 40. To testthis, she randomly selected 60 customers, and the average customer age was found to be 42.7 years.Assume the (population) standard deviation for customer age is 8 years. Using a 5% level ofsignificance, does the sample provide enough evidence to refute the claim made by the manager

The professior of a university believes that the average age of the bachelor students  is 23. However, the tutor belives that the average age of the bachelor students differs from 23. To test the claim, they randomly selected 100 students, the average age was found to be 24.2 years. Assume the population standard deviation for the student age is 6 years. At the 1% level of significance, what is the test statistics?

The marketing manager for a home mobility aids needed more information about the age profile of potential customers. The manager predicts that the average age of customers is greater than 70 years. A random sample of 25 customers is selected from various retirement villages and their age (in years) is recorded. This data is located in Sheet A of the Practice Data fileIs there sufficient evidence to support the manager’s claim? Use 0.05 level of significance.The hypothesis to test this claim is

Determine whether the given value is a statistic or parameter.A sample of 100 employees of a company is selected, and the average age is found to be 38 years.

In Exercise 2 of Tutorial 4, first we developed a confidence interval for the difference between the mean ages of purchasers and non-purchasers of a particular brand of toothpaste (part a), and then performed a t-test to see whether there was sufficient evidence to conclude that there was a difference in the mean age of purchasers and non-purchasers (part b). Based on the sample variances, in both cases we assumed that the two unknown population variances are different. Let’s check now whether this assumption is supported by the data.Namely, using the same data,a) Estimate the ratio of the two population variances with 95% confidence.b) Can we conclude at the 5% significance level that the population variances differ? What do you conclude if the significance level is increased to 10%?In parts (a) and (b) alike, do the calculations both manually and with R.