A machine fills bottles with a mean volume of 500 ml and standard deviation 4 ml. After servicing, a random sample of 25 bottles has mean volume 498.2 ml. Assume the standard deviation is unchanged.
(a) Test, at the 5% significance level, whether the mean volume has decreased.
(b) Find the critical region for the sample mean for this test.
(c) State the probability of a Type I error in this test.
From Paper 3: Pure and Statistics
1710 marks
A student collects data on daily hours of sunshine and the number of ice creams sold at a kiosk on 12 randomly chosen days. The product moment correlation coefficient is r = -0.62.
(a) Test, at the 5% significance level, whether there is evidence of correlation between hours of sunshine and ice cream sales. (Critical value for a two-tailed test at 5% with n = 12: 0.5760.)
(b) The student says this proves that sunshine reduces ice cream sales. Comment on this claim.
(c) The critical value for a two-tailed test at 1% with n = 12 is 0.7079. State, with a reason, whether your conclusion would change at the 1% level.
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This paper is written by Plasmo in the style of the AQA A-Level Maths exam. It is not a past paper and is not produced or endorsed by the exam board.