A manufacturer claims that a model of electric scooter has a battery charging time of 150 minutes (i.e. 2.5 hours). In order to test this claim, 2. electric scooters of that model were charged from empty to full battery. TE length of time for each scooter to charge fully was recorded in minutes. The results are summarised in Table 2.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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A manufacturer claims that a model of electric scooter has a battery
charging time of 150 minutes (i.e. 2.5 hours). In order to test this claim, 22
electric scooters of that model were charged from empty to full battery. The
length of time for each scooter to charge fully was recorded in minutes.
The results are summarised in Table 2.
Table 2 Summary statistics for the battery charging time (in minutes) of a
model of electric scooter
Sample size Mean Standard deviation
22
161
29
(a) What is the most appropriate version of the t-test if you want to test
the null hypothesis that the underlying population mean battery
charging time for this model of scooter is what the manufacturer claims
it to be, and the alternative hypothesis is that the underlying
population mean battery charging time is not what the manufacturer
claims it to be? Justify your choice.
(b) What are the number of degrees of freedom and the 5% critical value for
the most appropriate t-test applied to these data?
(c) Hence calculate a 95% confidence interval for the population mean
battery charging time for this model of electric scooter. Your answer
should be rounded to the nearest whole number.
(d) Based on your calculated 95% confidence interval, is it plausible that
the underlying population mean battery charging time is 150 minutes as
claimed by the manufacturer? Justify your answer.
Transcribed Image Text:A manufacturer claims that a model of electric scooter has a battery charging time of 150 minutes (i.e. 2.5 hours). In order to test this claim, 22 electric scooters of that model were charged from empty to full battery. The length of time for each scooter to charge fully was recorded in minutes. The results are summarised in Table 2. Table 2 Summary statistics for the battery charging time (in minutes) of a model of electric scooter Sample size Mean Standard deviation 22 161 29 (a) What is the most appropriate version of the t-test if you want to test the null hypothesis that the underlying population mean battery charging time for this model of scooter is what the manufacturer claims it to be, and the alternative hypothesis is that the underlying population mean battery charging time is not what the manufacturer claims it to be? Justify your choice. (b) What are the number of degrees of freedom and the 5% critical value for the most appropriate t-test applied to these data? (c) Hence calculate a 95% confidence interval for the population mean battery charging time for this model of electric scooter. Your answer should be rounded to the nearest whole number. (d) Based on your calculated 95% confidence interval, is it plausible that the underlying population mean battery charging time is 150 minutes as claimed by the manufacturer? Justify your answer.
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(d) Based on your calculated 95% confidence interval, is it plausible that
the underlying population mean battery charging time is 150 minutes as
claimed by the manufacturer? Justify your answer.
Transcribed Image Text:(d) Based on your calculated 95% confidence interval, is it plausible that the underlying population mean battery charging time is 150 minutes as claimed by the manufacturer? Justify your answer.
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