5 Observations over a long period of time have shown that the mid-day temperature at a particular place during the month of June is normally distributed with a mean value of 23.9 °C with standard...

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Extracted text: 5 Observations over a long period of time have shown that the mid-day temperature at a particular place during the month of June is normally distributed with a mean value of 23.9 °C with standard deviation 2.3 °C. An ecologist sets up an experiment to collect data for a hypothesis test of whether the climate is getting hotter. She selects at random 20 June days over a five-year period and records the mid-day temperature. Her results (in °C) are as follows. 20.1 26.2 23.3 28.9 30.4 28.4 17.3 22.7 25.1 24.2 15.4 26.3 19.3 24.0 19.9 30.3 32.1 26.7 27.6 23.1 (i) State the null and alternative hypotheses that the ecologist should use. (ii) Carry out the test at the 10% significance level and state the conclusion. (iii) Calculate an unbiased estimate of the population variance and comment on it.


Extracted text: (i) H,:H = 23.9°, H,: µ > 23.9° 5 (ii) z= 1.29, significant (iii) 20.6; the standard deviation 4.54 is much greater than 2.3 so the ecologist should be asking whether the temperature has become more variable.