a) People who diet can expect to lose an average of 3kg in a month. In a book, the authors
claim that people who follow a new diet will lose an average of less than 3kg in a month.
The weight losses of the 180 people in a random sample who had followed the new diet
for a month were noted. The mean was 2.7 kg and the standard deviation was 2.8kg.
ECON1005 Introductory Statistics
Semester 1 2022/23
Test the authors' claim at the 5% significance level, stating your null and alternative
hypotheses.
[6]
b) From a sample of 200 bread rolls from Ideal bakery, 95 of the were wheat. The manager
of the bakery claims that 49% of their rolls are wheat.
i.
Test at the 1% significance level to determine whether the true proportion is less
than 49%.
[6]
ii.
Create a 99% confidence interval for the proportion of all wheat bread rolls
produced from Ideal bakery.
[4]