Question

In previous years, the marks obtained in a French test by students attending Topnotch College have been modelled satisfactorily by a normal distribution with a mean of 65 and a standard deviation of 9. Teachers in the French department at Topnotch College suspect that this year their students are, on average, underachieving. In order to investigate this suspicion, the teachers selected a random sample of 35 students to take the French test and found that their mean score was 61.5 (a) Investigate, at the 5% level of significance, the teachers' suspicion. (b) Explain, in the context of this question, the meaning of a Type I error.(2 marks) (6 marks)

Answer 1

H_0: mu = 65 v/s H_i: mu < 65 under H_0 squareroot 35 (X-u)/9 tilde N(0, 1). This is our test statistic Reject H_0 of squareroot 35 (X-65)/9 < 1.64 [At < 70 level of significance] Test statistic is squareroot 35 (-3.5)/9 = -2.3007 Therefore, we reject the null hypothesis at 5% level of significance. b) The meaning of Type I error is that the population mean is 65 but the sample use have chosen is underachieving among the population.