A local authority in a city wants to reduce the amount of sugary drinks consumed by teenagers. Before an intervention program, the mean weekly consumption of sugary drinks per teenager was known to be 1820 ml1820\text{ ml}1820 ml, with a standard deviation of 450 ml450\text{ ml}450 ml.
After the program, a researcher surveys the first 600600600 teenagers they encounter at a local shopping mall to record their consumption.
State the sampling method used to collect the survey data.
Explain why this specific sample should not be used to conduct a formal hypothesis test.
A second, independent sample of 600600600 teenagers is selected using a random sampling method. This sample revealed a mean consumption of 1792 ml1792\text{ ml}1792 ml per week.
Investigate, at the 5%5\%5% level of significance, whether the intervention program has decreased the mean consumption of sugary drinks per teenager.
Assume that the consumption of sugary drinks is normally distributed and the standard deviation remains unchanged at 450 ml450\text{ ml}450 ml.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.