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.
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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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Transcribed Image 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.
Transcribed Image 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.
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