1. A researcher wanted to estimate the meancontributions made to charitable causes by all major companies. Arandom sample of 18 companies produced by the following data oncontributions (in millions of dollars) made by them.
1.8, 0.6, 1.2, 0.3, 2.6, 1.9, 3.4, 2.6, 0.2
2.4, 1.4, 2.5, 3.1, 0.9, 1.2, 2.0, 0.8, 1.1
Assume that the contributions made to charitablecauses by all major companies have a normal distribution.
a. What is the point estimate for the population mean?
b. Construct a 98% confidence interval for the populationmean.
c. What sample size would the researcher need to obtain a margin oferror of 100,000 for the same confidence level? (Assume that thesample standard deviation obtained from his original sample isequal to the population standard deviation.)
d. Prior to collecting the data, the researcher believed that themean contribution of all companies was less than $2.5 million. Fora significance level of 0.01, test the researchers hypothesis.
