Standard +0.3 This is a straightforward one-sample t-test with clear hypotheses (H₀: μ = 1010, H₁: μ < 1010). Students must calculate sample mean and standard deviation from 8 values, find the t-statistic, compare to critical value from tables, and conclude. It's a standard textbook application of hypothesis testing with small sample size, slightly above average difficulty only due to the calculation burden and need to recall the complete testing procedure.
A machine is set to fill bags with flour such that the mean weight is 1010 grams.
To check that the machine is working properly, a random sample of 8 bags is selected. The weight of flour, in grams, in each bag is as follows.
1010 1015 1005 1000 998 1008 1012 1007
Carry out a suitable test, at the 5\% significance level, to test whether or not the mean weight of flour in the bags is less than 1010 grams. (You may assume that the weight of flour delivered by the machine is normally distributed.)
(Total 8 marks)
A machine is set to fill bags with flour such that the mean weight is 1010 grams.
To check that the machine is working properly, a random sample of 8 bags is selected. The weight of flour, in grams, in each bag is as follows.
1010 1015 1005 1000 998 1008 1012 1007
Carry out a suitable test, at the 5\% significance level, to test whether or not the mean weight of flour in the bags is less than 1010 grams. (You may assume that the weight of flour delivered by the machine is normally distributed.)
(Total 8 marks)
\hfill \mbox{\textit{Edexcel S4 Q3}}