Hypothesis test via confidence interval for a proportion
The question provides a claimed population proportion and sample data, and asks the student to use a confidence interval to decide whether the claim should be questioned or rejected.
A study conducted in 2000 showed that the percentage of French people regularly consuming ice cream was 84\%. In 2010, out of 900 people surveyed, 795 of them declared consuming ice cream. Can we affirm, at the 95\% confidence level and based on the study of this sample, that the percentage of French people regularly consuming ice cream remained stable between 2000 and 2010?
The company sought to improve the quality of its production and claims that there are no more than $6\%$ defective light bulbs in its production. A consumer association conducts a test on a sample and obtains 71 defective light bulbs out of 1000.
In the case where there would be exactly $6\%$ defective light bulbs, determine an asymptotic confidence interval at the $95\%$ level for the frequency of defective light bulbs in a random sample of size 1000.
Do we have reasons to question the company's claim?
Part C - Satisfaction survey The company announces a satisfaction rate of $85\%$ for its customers who called and reached an operator. A consumer association wishes to verify this rate and surveys 1303 people. Among these, 1150 say they are satisfied. What do you think of the satisfaction rate announced by the company?