One-sample t-test, variance unknown

Test a hypothesis about the population mean when the population variance is unknown and must be estimated from the sample, using the t-distribution with n-1 degrees of freedom.

1 questions · Standard +0.3

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WJEC Further Unit 5 2019 June Q6
10 marks Standard +0.3
A manufacturer of batteries for electric cars claims that an hour of charge can power a certain model of car to travel for an average of 123 miles. An electric car company and a consumer, Hopcyn, both wish to test the validity of the manufacturer's claim.
  1. Explain why Hopcyn may want to use a one-sided test and why the car company may want to use a two-sided test. [2]
To test the validity of this claim, Hopcyn collects data from a random sample of 90 drivers of this model of car to see how far they travelled, \(X\) miles, on an hour of charge. He produced the following summary statistics. $$\sum x = 11007 \quad \sum x^2 = 1361913$$
    1. Assuming Hopcyn uses a one-sided test, state the hypotheses.
    2. Test at the 5\% significance level whether the manufacturer's claim is correct. [8]