Question 2 - A-Level Maths

Exam Board	Edexcel
Module	FS2 (Further Statistics 2)
Year	2022
Session	June
Topic	Hypothesis test of a normal distribution

A factory produces yellow tennis balls and white tennis balls. Independent samples, one of yellow tennis balls and one of white tennis balls, are taken. The table shows information about the weights of the yellow tennis balls, \(Y\) grams, and the weights of the white tennis balls, \(W\) grams.

	Sample size	Mean weight of random sample (grams)	Known population standard deviation of weights (grams)
Yellow tennis balls	120	57.2	1.2
White tennis balls	140	56.9	0.9

Find a 95\% confidence interval for the mean weight of yellow tennis balls. Jamie claims that the mean weight of the population of yellow tennis balls is greater than the mean weight of the population of white tennis balls. A test of Jamie's claim is carried out.
1. Specify the approximate distribution of \(\bar { Y } - \bar { W }\) under the null hypothesis of the test.
2. Explain the relevance of the large sample sizes to your answer to part (i).
Complete the hypothesis test using a \(5 \%\) level of significance. You should state your hypotheses and the value of your test statistic clearly.